Question

If sum of the roots of the quadratic equation ax² + bx + c = 0 equal to the sum of the square of their reciprocals then prove that c÷a,a÷b,b÷c are in A.P.​

Answer 1

Answer:

ax2+bx+c=0

The sum of roots are α+β=a−b=α21+β21=(αβ)2α2+β2=(αβ)2(α+β)2−2(αβ)

The product of the roots are αβ=ac

Substituting α+β=a−b and αβ=ac, we get

a−b=(ac)2(a−b)2−2(ac)a−b=