Question

Determine the zeros of f(x) = x3 – 12x2 + 28x – 9 ?

Answer 1

f(x) = x3 – 12x2 + 28x – 9 =0
The only possible rational real roots are +1, -1, +3, -3, +9, -9. So evaluate the function at these values and see if any of these make the function equal to zero. (These are the only possible real roots because we take all the possible factors of 9 and divide them by all the possible factors of 1...the coordinates of the last and the first terms.)
f(9)=0 so 9 is a root.
Perform Synthetic Division.

9/ 1 -12 28 -9
9 -27 9
_________________
1 -3 1 0


We now have f(x) = (x-9)(x^2 -3x + 1) You would now use the quadratic formula to factor the second part. I will leave that for you to work on.

Answer 2

Thank you !!