If the roots of the quadratic equation $ (b-c) x^{2}+(c-a) x+(a-b)=0 $ are equal, then $ a, b, c $ are in

Question

If the roots of the quadratic equation $ (b-c) x^{2}+(c-a) x+(a-b)=0 $ are equal, then $ a, b, c $ are in, A.P., G.P., H. P., None of these

MARKS App · Accepted Answer

Given equation: b - c x 2 + c - a x + a - b = 0 Putting x = 1 , we get b - c + c - a + a - b = 0 So, x = 1 is a root but both roots are equal so both roots are 1 , 1 . Now sum of roots 1 + 1 = - c - a b - c ⇒ 2 = - c - a b - c ⇒ 2 b - 2 c = - c + a ⇒ 2 b = a + c ⇒ a , b , c are in A . P .

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