3 square root of 250 in simplest radical form

For what value of k is there one solution to the given quadratic equation (k+1)x²+4kx+2=0.

andriy [413]

Answer:

If $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

The signal of $\bigtriangleup$ determines how many real roots an equation has:

$\bigtriangleup > 0$ : Two real and different solutions

$\bigtriangleup = 0$ : One real solution

$\bigtriangleup < 0$ : No real solutions

In this problem, we have the following second order polynomial:

$(k+1)x^{2} + 4kx + 2 = 0$ .

This means that $a = k+1; b = 4k; c = 2$

It has one solution if

$\bigtriangleup = 0$

$b^{2} - 4ac = 0$

$16k^{2} -8(k+1) = 0$

$16k^{2} - 8k - 8 = 0$

We can simplify by 8

$2k^{2} - k - 1 = 0$

The solution is:

$k = 1$ or $k = -\frac{1}{2}$

So, if $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

4 0

3 years ago

What is 4-2x+8+5x simplified

sveta [45]

Answer: it is 3 • (x + 4)

Step-by-step explanation: We move all terms to the left:

4-2x+8-(+5x)=0

We add all the numbers together, and all the variables

-2x-(+5x)+12=0

We get rid of parentheses

-2x-5x+12=0

We add all the numbers together, and all the variables

-7x+12=0

We move all terms containing x to the left, all other terms to the right

-7x=-12

x=-12/-7

x=1+5/7We move all terms to the left:

4-2x+8-(+5x)=0

We add all the numbers together, and all the variables

-2x-(+5x)+12=0

We get rid of parentheses

-2x-5x+12=0

We add all the numbers together, and all the variables

-7x+12=0

We move all terms containing x to the left, all other terms to the right

-7x=-12

x=-12/-7

x=1+5/7

6 0

3 years ago

Read 2 more answers

What is the differnce between (-4)-6

EastWind [94]

Answer:

24

Step-by-step explanation:

(-4) -6? well it equals 24 because a negative plus a negative equals a positive.

Hope my answer has helped you! If not i'm sorry.

6 0

3 years ago

Karla has a cylindrical candy jar that is 5 inches tall and has a radius of 1.25 inches. The candy jar is 75% full. How much vol

elena-s [515]

Answer:

I think the answer is 18.3984375 inches

8 0

3 years ago

A college professor reports that students who finish exams early tend to get better grades than students who hold on to exams un

s344n2d4d5 [400]

Answer:

The correlation between exam score and amount of time spent on the exam is an example of a <u>negative correlation</u>.

Step-by-step explanation:

Consider the provided statement.

College professor reports that students who finish exams early tend to get better grades than students who hold on to exams until the last possible moment.

That means the student who finish the exam early will get the highest marks. One who finish after the first student will get second highest mark and the one who finish in the end will get the least marks.

Now consider time as first variable and marks as second variable.

That means as the first variable increase the second variable decreases.

According to the definition of Negative correlation: It is a relationship between two variables in which one variable increases as the other decreases, and vice versa.

Hence, the correct answer is negative correlation.

7 0

3 years ago