Mathematics: 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

moderate negative correlation...

Which of the following possible rational roots is

metatiley

06.02.2022

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.

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