Question

Determine algebraically the zeros of f(x)=3x^3+21x^2+36x

Answer 1

Answer:

The zeros of the given polynomial function f(x) are -3,0,-4

Step-by-step explanation:

Given polynomial is $f(x)=3x^3+21x^2+36x$

To find the zeros of the given polynomial:

First equate the polynomial function f(x) to zero

That is $f(x)=3x^3+21x^2+36x=0$

By synthetic division we can solve it

-3_| 3      21       36     0

      0       -9      -36    0

   _____________________

      3      12        0        0

      Therefore x+3 is a factor

    That is x=-3 is a zero

    $3x^2+12x=0$

    $3x(x+4)=0$

    3x=0 or x+4=0

    Therefore x=0 or x=-4

    Therefore the zeros are -3,0,-4