Suppose a quadratic equation has the form x^2 + x + c = 0. Show that the constant c must be less than 1/4 in order for the equation to have two real solutions.

Suppose A Quadratic Equation Has The Form X^2 + X + C = 0. Show That The Constant C Must Be Less Than

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is

b² - 4ac > 0

x² + x + c = 0 ← is in standard form

with a = 1, b = 1, c = c , then

b² - 4ac > 0

1² - (4 × 1 × c) > 0

1 - 4c > 0 ( subtract 1 from both sides )

- 4c > - 1

Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.

c < [tex]\frac{1}{4}[/tex]


Related Questions

What is the vertical shift for the absolute value function below f(x) =9 |x+1|+2

Answers

Answer:

Slide UP 2

Step-by-step explanation:

In the equation,

f(x) = 9|x+1| + 2

There are three transformations of the parent function f(x)=|x| (this is the simplest form of this function, it's a v-shaped graph)

The 9 in front will vertically stretch the graph and make it look like a "skinny" v-shaped graph.

The +1 in close to the x inside the absolute value bars |x+1| will shift (slide) the graph to the left (it's the opposite of what you might think-- 'plus' shifts the graph left and 'minus' shifts the graph right)

The +2 at the end is the transformation you're looking for. It slides the graph as you would expect UP 2 units. If it was a minus it would shift the graph down instead.

Find the value of 5x + 6 when x = -2

Answers

Answer:

- 4

Step-by-step explanation:

Substitute x = - 2 into the expression

5x + 6 = 5(- 2) + 6 = - 10 + 6 = - 4

find the mean of 98 100 100 100 100 100​

Answers

Answer:

the mean of this sequence of numbers is 99

Answer:

it is 99

Step-by-step explanation:

Please help!! markup and markdown word problems.


1. A boat is marked up 20% on the original price. The original price was $50. What is the sale price of the boat before sales tax?


2. Fred buys a video game disk for $4. There was a discount of 20%. What is the sales price?


3. A painting is on sale at 50% off. The sale price is $320. What was the original price?

Answers

Answer:

Step-by-step explanation:

1. A boat is marked up 20% on the original price. The original price was $50. What is the sale price of the boat before sales tax?

$50(1+0.20) = $60

                                                                                 

2. Fred buys a video game disk for $4. There was a discount of 20%. What is the sales price?

$4(1-0.2) = $3.20

3. A painting is on sale at 50% off. The sale price is $320. What was the original price?

X*(1-0.5) = $320

X = $320/0.5

X = $640

Find the 53" term of the following arithmetic sequence.
3, 11, 19, 27, ...

Answers

Answer:

419

Step-by-step explanation:

a=3

d=11-3=8

[tex]a_{n}=a+(n-1)d\\n=53\\a_{53}=3+(53-1)*8\\=3+52*8\\=3+416\\=419[/tex]

If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?

Answers

Answer:

See below

Step-by-step explanation:

(-4,0) is the solution to x+4=0

(0,0) is the solution to x=0

(2,0) is the solution to x-2=0

Therefore, (x+4)(x-2)(x) = (x²-2x+4x-8)(x) = (x²+2x-8)(x) = x³+2x²-8x is the function that has the given zeroes

1) Solve for x (11 - 2*) 7 = 21​

Answers

ok done. Thank to me :>

if you roll a fair 6-sided die 9 times, what is the probability that at least 2 of the rolls come up as a 3 or a 4?

Answers

Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.

For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.

In this problem:

There are 9 rolls, hence [tex]n = 9[/tex].Of the six sides, 2 are 3 or 4, hence [tex]p = \frac{2}{6} = 0.3333[/tex]

The desired probability is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{9,0}.(0.3333)^{0}.(0.6667)^{9} = 0.026[/tex]

[tex]P(X = 1) = C_{9,1}.(0.3333)^{1}.(0.6667)^{8} = 0.117[/tex]

Then:

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.026 + 0.117 = 0.143[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.143 = 0.857[/tex]

0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.

For more on the binomial distribution, you can check https://brainly.com/question/24863377

You plant 9 rows of different bulbs in a garden. For each row, you use the rule, “onion, onion, garlic, flower.” How many garlic and flower bulbs do you plant altogether? How many bulbs do you use in all?

Answers

Answer: Who the actual fudge gardens anymore????? like what are you an old lady? ur name edna? ethel? doreen? geez louise u are old.

Step-by-step explanation:

In class A, 17 students in a class of 25 passed an exam. In class B, 13 out of 20 passed. In class C, 7 out of 10 passed. Which class is the best class?

Answers

Answer:

class C

Step-by-step explanation:

a=(17/25)=0.68

b=(13/20)=0.65

c=(7/10)=0.7

Using substitution, evaluate the expression b-a, if a = -14 and b = -7.
O 21
O -21
-7
7.
Please help

Answers

a = -14
b = -7
b - a
(-7) - (-14)
-7 + 14
7
So the answer is 7

20. Write an expression: Alexis has $10 less than twice the amount that David has. If David has
x dollars, write an expression to represent the amount that Alexis has.

Answers

Answer:

2x - 10

Step-by-step explanation:

'x' = amount David has

Alexis = 2x - 10

15=x/4 - 3 how do i solve

Answers

Answer: the answer is x=72

Step-by-step explanation:

Step 1: simplify both sides we know 15=x/4 -3 (the x holds a invisible 1)

the equation should look something Like: 15=1/4x-3 then FLIP the equation such as:

1/4x-3=15 then add 3 on both sides so 15+3=18

step 2: our equation is now 1/4x=18  (we see 4 is being divided the opposite of division is multiply) therefor multiply the 18 with 4

18*4=72 which means x=72

Answer as soon as possible I’ll give 5 stars!!!

Answers

Answer:

B

Step-by-step explanation:

2 times x is 2x

2*8=16

its B

Hey there!

2(x + 8)

DISTRIBUTE 2 WITHIN THE PARENTHESES

= 2(x) + 2(8)

= 2x + 16

Therefore, your answer should be: 2x + 16

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

what is solve 10<-2/3(9+12b)

Answers

Ok done. Thank to me:>

Writing a ratlo as a percentage
Manuel has ridden 8 miles of a bike course. The course is 20 miles long. What percentage of the course has Manuel ridden so far?
0
se
%
X 5
?

Answers

8/20 = (x5) 40/100
40/100 = 40%
answer = 40%

The formula N(x) = x2 -2x + 2016 represents the number N of gang-related homicides across the country x years after 2017. According to this formula, in what year will the number of gang-related homicides be 2051?

Answers

Answer:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:

(

1

,

2015

)

Focus:

(

1

,

8061

4

)

Axis of Symmetry:

x

=

1

Directrix:

y

=

8059

4

x

y

1

2019

0

2016

1

2015

2

2016

3

2019

Step-by-step explanation:

The number of gang-related homicides in 2051 will be 3,104.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

N(x) = x² -2x + 2016

N represents the number of gang-related homicides across the country x years after 2017.

Then the number of gang-related homicides be 2051 will be given as,

N(2051 - 2017) = (2051 - 2017)² - 2(2051 - 2017) + 2016

N(34) = 34² - 2(34) + 2016

N(34) = 1156 - 68 + 2016

N(34) = 3,104

The quantity of pack-related homicides in 2051 will be 3,104.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.

Answers

Answer:

\huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂ \huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂ \huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂ \huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂ \huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂ \huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂ \huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂ \huge\purple{ 〇 }〇 \huge\blue{ △ }△ \huge\orange{ ☆ }☆ \huge\pink{ ☂ }☂

Answer:

Negative correlation

Step-by-step explanation:

As TV hours increase, exercise hours decrease.

HELP MEEEEEEEEEEEEEEEEE!
X +(X+1)+...+2020+2021=2021

Answers

If x is an integer, and

x + (x + 1) + … + 2020 + 2021 = 2021

then of course

x + (x + 1) + … + 2020 = 0

and we can write the left side as a sum,

[tex]\displaystyle \sum_{k=0}^n (x+k) = 0[/tex]

with n such that x + n = 2020. (Notice that there are n + 1 terms in the sum.) Then x = 2020 - n, so that

[tex]\displaystyle \sum_{k=0}^n (2020 - n + k) = (2020 - n) \sum_{k=0}^n 1 + \sum_{k=0}^n k= 0[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = 1 + 1 + 1 + \cdots + 1 = n[/tex]

[tex]\displaystyle \sum_{k=1}^n 1 = 1 + 2 + 3 +  \cdots + n = \frac{n(n+1)}2[/tex]

Then

[tex]\displaystyle (2020 - n) (n + 1) + \frac{n(n+1)}2= 0[/tex]

Solve for n :

(2020 - n) (n + 1) + n (n + 1) / 2 = 0

4040 + 4039 n - n² = 0

(n - 4040) (n + 1) = 0

⇒   n = 4040   or   n = -1

But we are taking the sum of a positive number of terms, so n = 4040.

Then since x + n = 2020, it follows that x = 2020 - 4040 = -2020.

What’s 12.71 divided 6.2?

Answers

Answer:

2.05

Step-by-step explanation:

12.71/6.2=2.05

The value of the expression 12.71 ÷ 6.2 using the division property will be 2.05.

What is Algebra?

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

12.71 and 6.2

Then the division of the decimal numbers 12.71 and 6.2 will be given by putting a divide sign between them. Then we have

⇒ 12.71 ÷ 6.2

⇒ 12.71 / 6.2

⇒ 2.05

The worth of the articulation 12.71 ÷ 6.2 utilizing the division property will be 2.05.

More about the Algebra link is given below.

https://brainly.com/question/953809

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If a number has 8 as a factor, then both 2 and 4 are factors

Answers

yes that is correct

help please its overdue

Answers

Answer:

B) 4cm

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Segments CD, GH, and JK intersect point A.

Answers

Answer: HK

Step-by-step explanation:

Three more than a positive number is twenty less than it’s square. What is the number ?

Answers

Answer:

the +ve no. = 2

Step-by-step explanation:

let the number be x - 3

three more than a positive number = x

acc. to condition

x^{2}x

2

- 20 = x

x^{2} - x - 20 = 0x

2

−x−20=0

x^{2} - 5x + 4x - 20 = 0x

2

−5x+4x−20=0

x(x - 5) +4(x - 5) = 0x(x−5)+4(x−5)=0

(x+4)(x-5) = 0(x+4)(x−5)=0

Case 1

x + 4 = 0x+4=0

x = -4x=−4

the Number cannot be negative because the condition given in question

Case 2

x - 5 = 0x−5=0

x = 5x=5

Hence, the positive number

= x - 3=x−3

= 5 - 3=5−3

= 2=2 hope i help you

A car can travel 300 miles on 12 gallons of gas. At this rate, how many miles can the car travel on 1 gallon of gas?


12 miles

12 miles

25 miles

25 miles

120 miles

120 miles

312 miles

312 miles

Answers

Answer:

25 miles?

Step-by-step explanation:

Help!! Simplify the expression?

Answers

Answer:

Here is my answer I have solved hope this helps

Howie wants to get a car loan with 4% simple interest rate. If the car costs $25,000, how much would Howie need to pay back at the end of one year, including the interest?

Answers

The amount Howie will pay back at the end of one year is $26000.00

The given parameters are:

[tex]P =25000[/tex] -- the principal amount

[tex]R = 4\%[/tex] -- the interest rate

[tex]T=1[/tex] --- the duration

The amount to pay back in this duration is then calculated using:

[tex]A = P(1 + RT)[/tex]

So, we have:

[tex]A = 25000(1 + 4\% \times 1)[/tex]

[tex]A = 25000(1 + 4\% )[/tex]

Express percentage as decimal

[tex]A = 25000(1 + 0.04)[/tex]

[tex]A = 25000(1 .04)\\[/tex]

Multiply

[tex]A = 26000[/tex]

Hence, the amount to pay back is $26000.00

Read more about simple interest at:

https://brainly.com/question/1115815

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8593 g and a standard deviation of 0.0511 g. A sample of these candies came from a package containing 464 ​candies, and the package label stated that the net weight is 396.1 g.​ (If every package has 464 ​candies, the mean weight of the candies must exceed 396.1 464=0.8537 g for the net contents to weigh at least 396.1 ​g.)

Answers

Answer:

The package label stated that the net weight is 381.8g If every package has ... brand of candies have a mean weight of 0.8616g and a standard deviation of ...

Chi is planning to put a path of paving stones through her flower garden. The flower garden is a square with sides of 15 feet. How many feet long will the path be? Round your answer to one decimal place.

Answers

[(15×2)+(15×2)]=60=6.0

If 108 is added to a number, it will be 5 times as large as it was originally. Find the number.

Answers

Answer:

27

Step-by-step explanation:

let th original number=x

x+108=5x

5x-x=108

4x=108

x=108/4=27

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