Write an equation based on the graph.

Which of the following represents the zeros of f(x) = 2x3 − 5x2 − 28x + 15?

likoan [24]

$\mathrm{Use\:the\:rational\:root\:theorem}$

$a_0=15,\:\quad a_n=2$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:3,\:5,\:15,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:3,\:5,\:15}{1,\:2}$

$-\frac{3}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+3$

$\mathrm{Compute\:}\frac{2x^3-5x^2-28x+15}{x+3}\mathrm{\:to\:get\:the\:rest\:of\:the\:eqution:\quad }2x^2-11x+5$

$=\left(x+3\right)\left(2x^2-11x+5\right)$

$Factor: 2x^2-11x+5$

$2x^2-11x+5=\left(2x^2-x\right)+\left(-10x+5\right)$

$=x\left(2x-1\right)-5\left(2x-1\right)$

$2x^3-5x^2-28x+15=\left(x+3\right)\left(x-5\right)\left(2x-1\right)$

$\left(x+3\right)\left(x-5\right)\left(2x-1\right)=0$

$\mathrm{Using\:the\:Zero\:Factor\:Principle:}$

thus zeros of f(x) is

$x=-3,\:x=5,\:x=\frac{1}{2}$

5 0

3 years ago

Read 2 more answers

What is the perimeter of a square with an area of 81 cm2

tatyana61 [14]

Answer:

36 cm

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Bruno claims that the solution to the linear equation −3(2x+6)+25=1 is x=1. He shows the steps below to justify his solution.

jonny [76]

Answer:

Bruno is correct x=1

Step-by-step explanation:

-3(2x+6)+25=1

-6x-18+25=1

-6x+7=1

-6x=-6

1=x

6 0

3 years ago

Sa = 2(pi)(r)(h) + 2(pi)(r^2) v = (pi)(r^2)(h) find the surface area and the volume.

LenKa [72]

If Sa=2πrh+2π $r^{2}$ v=π $r^{2}h$ then the surface area is π $r^{2} h$ and volume is

(rh-2h)/2r.

Given Sa=2πrh+2π $r^{2} v$ =π $r^{2}h$ .

We have to find surface area and volume from the given expression.

Volume is basically amount of substance a container can hold in its capacity.

First we will find the value of v from the expression. Because they are in equal to each other, we can easily find the value of v.

2πrh+2π $r^{2}$ v=π $r^{2}$ h

Keeping the term containing v at left side and take all other to right side.

2π $r^{2}$ v=π $r^{2}h$ -2πrh

v=(π $r^{2}$ h-2πrh)/2π $r^{2}$

v=π $r^{2} h$ /2π $r^{2}$ -2πrh/2π $r^{2}$

v=h/2-h/r

v=h(r-2)/2r

Put the value of v in Sa=2πrh+2π $r^{2} v$

Sa=2πrh+2π $r^{2}$ *h(r-2)/2r

=2πrh+2πrh(r-2)/2

=2πrh+πrh(r-2)

=2πrh+π $r^{2}$ h-2πrh

=π $r^{2}$ h

Hence surface area is π $r^{2}$ h and volume is h(r-2)/2.

Learn more about surface area at brainly.com/question/16519513

#SPJ4

6 0

2 years ago

Solve the quadratic formula <br> 2x^2+9x=-7

andriy [413]

Answer:

Step-by-step explanation:

2x² + 9x = -7

2x² + 9x + 7 = 0

When we multiply we should get 2*7 = 14 and when we add we should get 9. Find the factors of 14 ---> 1,2,7,14. Factors are 2,7 as when we multiply we get 14 and we we add, get 9

2x² + 2x + 7x + 7 = 0

2x( x + 1) + 7 (x + 1) = 0

(x + 1)(2x + 7) = 0

5 0

4 years ago