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Nature of Roots of a Cubic Polynomial Using Derivatives

α, β are the ...

Question

$α, β$ are the roots of $a x^{2} + b x + c = 0 a n d γ, δ a r e t h e r o o t s o f p x^{2} + q x + r = 0 a n d D_{1}, D_{2}$ be the respective discriminants of these equations. If $α, β, γ, a n d δ$ are in A.P. then $D_{1} : D_{2} = (w h e r e α, β, γ δ, ϵ R & a, b, c, p, q, r ϵ R)$

A

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B

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C

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D

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Solution

The correct option is A

$β = α + d, γ = α + 2 d, δ = α + 3 d d^{2} = \frac{D_{1}}{a^{2}} = \frac{D_{2}}{p^{2}}$

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