If the roots of $a x 2 + b x + c = 0$ are in the ratio $m : n$ , then:

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mnb 2 = (m + n) ac

mnb 2 = (m + n) 2 ac

None of these.

answer is C.

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Detailed Solution

Concep- Find the product of the roots and the sum of the roots for the given equation first. Assume that my and ny are the roots. After that, modify the equation by adding the value of y from the sum equation to the product of the roots.

α β = m n

or by ratio proportion theory,

α m = β n = α + β m + n = α β mn

∴ mn (α + β) 2 = α β (m + n) 2

mn − b a 2 = (m + n) 2 c a

mnb 2 = ac (m + n) 2

Hence, the correct answer is option 3.

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