Question

alpha beta gamma are zeros of cubic polynomial x^3-12x^2+44x+c. if alpha beta gamma are in Ap find the value of c class 10

Answer 1

(x-alpha) (x-beta)(x-gama) = x^3 - 12 x^2 + 44x+c. So x^3 - x^2 (alpha+beta+gama)+ a(alphabeta+betagamma+gamma alpha)=alpha beta gama = x^3 - 12 x^2+44x+c, then alpha+beta+gama = -12.