hello all,
i hope this question is in the right board, anyhow, here is my problem:
if is divisible by both and , find the values of p and q
thanks
"if is divisible by both and , find the values of p and q."
Not so ELEGANT SOLUTION:
Notice that x^3 + px + q = (x - a)(x - b)(x - c) = (x - 3)(x + 2)(x - k)
that the coefficient of x^2 is ZERO, that means the sum of its roots is ZERO.
then, -(-3 + 2 - k) = 0, or
3 - 2 + k = 0,
k = -1; thus the 3 roots are, -2, -1 and 3.
p = (-2)(-1) + (-2)(3) + (-1)(3) = 2 - 6 - 3 = 2 - 9 = -7
q = -(-2)(-1)(3) = -6
x^3 -7x - 6 = (x - 3)(x + 2)(x + 1).