Question

Which of the following possible rational roots is a root of the function f(x)=x^3-3x^2+5x-15? *
5 points
-3
-1
1
3

Answer 1

Given:

The function is

$f(x)=x^3-3x^2+5x-15$

To find:

The root of the function from the given possible roots.

Solution:

We have,

$f(x)=x^3-3x^2+5x-15$

At x=-3,

$f(-3)=(-3)^3-3(-3)^2+5(-3)-15$

$f(-3)=-27-27-15-15$

$f(-3)=-84\neq 0$

At x=-1,

$f(-1)=(-1)^3-3(-1)^2+5(-1)-15$

$f(-1)=-1-3-5-15$

$f(-1)=-24\neq 0$

At x=1,

$f(1)=(1)^3-3(1)^2+5(1)-15$

$f(1)=1-3+5-15$

$f(1)=-12\neq 0$

At x=3,

$f(3)=(3)^3-3(3)^2+5(3)-15$

$f(3)=27-27+15-15$

$f(3)=0$

Since, the value of given function is 0 at only x=3, therefore 3 is a root of given function.

Hence, the correct option is D.