Question

Find all of the zeros of the function f(x) = x^3 + 5x^2 + 6x. If there is more than one answer, enter your answers as a comma separated list. If there are no zeros, enter NONE. Enter exact answers, not decimal approximations. x =

Answer 1

Answer:

There are more than one zero i.e. three zeros of the given polynomial.

            The zeros are:

                        $x=0,-2,-3$

Step-by-step explanation:

We are given a function f(x) by:

             $f(x)=x^3+5x^2+6x$

We know that the zeros of the function f(x) are the possible values of x at which the function is equal to zero.

Hence, when f(x)=0 we have:

$x^3+5x^2+6x=0\\\\i.e.\\\\x^3+3x^2+2x^2+6x=0\\\\i.e.\\\\x^2(x+3)+2x(x+3)=0\\\\i.e.\\\\(x^2+2x)(x+3)=0\\\\x(x+2)(x+3)=0\\\\i.e.\\\\x=0\ or\ x=-2\ or\ x=-3$