find the roots of the function f(x)=2x^3+4x^2+8

Question

f(x)=2x^3+4x^2+8

Answer 1

Brandy, I like to use synthetic division to determine the factors in which also contain the roots.

 

Since all the coefficients of the function are positive, than all the real roots would be negative.

 

Lets try -1.

 

-1  2   4   0   8

         -2  -2  2

     2   2  -2  10   This indicates -1 is not a root.

 

Lets try -2

 

  -2   2   4   0   8

            -4   0  0

        2   0   0   8  Nope, -2 is not a root.  This is where I use a graphing calculator.

 

It turns out the function only has one real root, and it lies between -3 and -2, yet it is closer to -3. 

I used a computer algorithm to determine the approximate root in which is -2.594. 

 

Hope this helps.