Question

The roots of the equation a(b - c) x2 + b( c-a) x + c(a - b) = 0 are

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Answer 1

ANSWER

As we know that for the quadratic equation ax^2+bx+c=0, roots will be equal if

D=B^2 −4AC=0

Therefore, for the equation,

a(b−c)x2+b(c−a)x+c(a−b)=0

A=a(b−c),B=b(c−a),C=c(a−b)

D=0

B^2-4AC=0

(b(c−a))^2-4(a(b−c))(c(a−b))=0

⇒ab+bc=2ac

Hence a,b and c are in HP.

HERE IS UR ANSWER