Question

If f(1) = 0, what are all the roots of the function f (x) = x cubed 3 x squared minus x minus 3? Use the Remainder Theorem. X = –1, x = 1, or x = 3 x = –3, x = –1, or x = 1 x = –3 or x = 1 x = –1 or x = 3.

Answer 1

All the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.

What is polynomial?

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The function given in the problem is,

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

If f(1) = 0

$f(1)=(1)^3+3(1)^2-(1)-3\\f(1)=1+3-1-3\\f(1)=0$

Thus, (x-1) is one of the factor of polynomial. Equate the polynomial equal to the zero, to find other roots as,'

$x^3+3x^2-x-3=0\\x^2(x+3)-1(x+3)=0\\(x+3)(x^2-1)\\(x+3)(x+1)(x-1)=0$

Equate all the groups to zero to find the roots as,

$x+3=0, x=-3\\x+1=0, x=-1\\x-1=0, x=1$

Hence, all the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.

Learn more about polynomial here;

brainly.com/question/24380382