real and imaginary zeros

Question

Find all the real and imaginary zeros for the polynomial function. 

f(x)=x^2+8x^2+5x-14

What are the real and imaginary zeros of (f)=x^3+8x^2+5x-14?

 

 

help is greatly appreciated, thank you!

Answer 1

f(x) = x³+8x²+5x-14

 

By inspection, we see that 1 is a root.  

 

Divide synthetically by x-1:

 

1⌋     1       8      5      -14

    _______1____9____14

        1       9     14       0

 

So, f(x) = (x-1)(x²+9x+14)

 

To find the remaining roots, set x²+9x+14 = 0

 

    x = [-9 ±√24]/2 = [-9 ± 2√6]/2

 

The roots are:  1, (-9+2√6)/2, (-9-2√6)/2