jmc

Question

The equation x^3 - 9x^2 + 8x +2 = 0 has three real roots p, q, r. Find 1p^2 + 1q^2 + 1r^2.

Accepted Answer

From Vieta's relations, we have p+q+r = 9, pq+qr+pr = 8 and pqr = -2. So align* 1p^2 + 1q^2 + 1r^2 = (pq + qr + rp)^2 - 2 (p + q + r)(pqr)(pqr)^2 = 8^2 - 2 9 (-2)(-2)^2 = 25. align*