If two roots of the equation x3-p x2+q x-r=0 are equal in magnitude but opposite in sign, then:

Question

If two roots of the equation x3-p x2+q x-r=0 are equal in magnitude but opposite in sign, then: (A) p r=q (B) q r=p (C) p q=r (D) p2 q2=r

Tardigrade Admin · Accepted Answer

Let the roots be α, β,-β then α+β-β=p ⇒ α=p.....(1) and α β-α β-β2=q ⇒ β2=-q..........(2) also -α β2=r ⇒ p q=r [using (1)].

Q. If two roots of the equation $x^{3} - p x^{2} + q x - r = 0$ are equal in magnitude but opposite in sign, then: