Question

Consider the function f(x)=x3+6x2+11x+6.

If f(x)=0 for x=−3, for what other values of x is the function equal to 0? List the values separated by commas. Do not include the zero x=−3 in your answer.

Answer 1

For x = -1, -2 the function f(x) is equal to 0

Solution:

Given function is:

$f(x) = x^3 + 6x^2 + 11x+6$

We have to find values of x for which the function is equal to 0

Find the zeros of function

$x^3 + 6x^2 + 11x+6 = 0\\\\(x+1)(x^2+5x+6) = 0\\\\(x+1)(x^2 + 2x + 3x + 6) = 0\\\\(x+1)((x^2+2x) + 3(x+2)) = 0\\\\(x+1)(x(x+2) + 3(x+2)) = 0\\\\Factor\ the\ common\ term\\\\(x+1)(x+2)(x+3) = 0$

Thus the zeros are:

x = -1

x = -2

x = -3

Thus for x = -1, -2, -3 the function f(x) is equal to 0