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 se

Question

olasank [31]

3 years ago

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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 se

parated list. If there are no zeros, enter NONE. Enter exact answers, not decimal approximations. x =

Mathematics

1 answer:

suter [353] · Answer 1 · 2022-04-25T11:27:57+03:00

<h2>Answer:</h2>

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

The zeros are:

$x=0,-2,-3$

<h2>Step-by-step explanation:</h2>

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:

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