If the sum of any two roots of the equation x 3 + p x 2 + q x + r = 0 is zero, then

Step-by-step solution

Given: x 3 + p x 2 + q x + r = 0 Let α ,   β   &   γ are the roots of the given equation then α + β + γ = - p     . . . i It is given that sum of any two roots is zero. So, let β + γ = 0 Then, from i , we get α = - p     . . . i i Since, α is also the root of the given equation therefore α 3 + p α 2 + q α + r = 0 ⇒ - p 3 + p p 2 - p q + r = 0 ⇒ p q = r