The equation: x^3 - 3x^2 - 10x + 24 = 0
has roots: 2, "h" and "k"
Determine a quadratic equation whose roots are "h" - "k" and "hk"
How do you do it?
The anwser is: x^2 + 5x -84 = 0
I'm guessing that you can solve for h and k, by first dividing by x-2, and the factoring the resulting polynomial. Say that h = 3 and k = -4. Then h-k = 3-(-4) = 7. hk = -12. Create the two polynomials corresponding to the roots.
(x-7)(x+12). Multiply it out to get the answer.
(I didn't solve the polynomial, I worked backwards to get the answer, but the approach is the same.)