Question

One root of f(x)=x^3-9x^2+26x-24 is x = 2. What are all the roots of the function? Use the Remainder Theorem.

(options)-- x = 2, x = 3, or x = 4 x = –2, x = –3, or x = –4 x = 1, x = 2, x = 3, or x = 13 x = –1, x = –2, x = –3, or x = –13

Answer 1

A

Explanation:

Answer 2

`x=3` or
`x=4`

Explanation:

the given function is;

`f(x)=x^3-9x^2+26x-24`

According to the rational roots theorem, the possible rational roots are;

`\pm1,\pm2\pm3,\pm4,\pm6,\pm8,\pm12,\24`.

According to the Remainder Theorem, if
`f(a)=0`, then
`x=a` is a zero of the polynomial.

`f(3)=3^3-9(3)^2+26(3)-24`

`f(3)=27-81+78-24`

`f(3)=24-24=0`

Also,

`f(4)=4^3-9(4)^2+26(4)-24`

`f(4)=64-144+104-24`

`f(4)=64-64=0`

Therefore the other roots are;

`x=3,x=4`