If the roots of the equation ax2 + ex + c = 0 are in the ratio p : q, then pq+qp+ca=

Given αβ=pqHere, α+β=−ca,αβ=caNow, pq+qp+ca=αβ+βα+ca=α+βαβ+ca=−caca+ca=−ca+ca=0Hence, the result.

If the roots of the equation ax2 + ex + c = 0 are in the ratio p : q, then pq+qp+ca=

Given αβ=pqHere, α+β=−ca,αβ=caNow, pq+qp+ca=αβ+βα+ca=α+βαβ+ca=−caca+ca=−ca+ca=0Hence, the result.

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If the roots of the equation ax² + ex + c = 0 are in the ratio p : q, then $\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} + \sqrt{\frac{c}{a}}$ =

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answer is D.

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Detailed Solution

Given $\frac{α}{β} = \frac{p}{q}$

Here, $α + β = - \frac{c}{a}, α β = \frac{c}{a}$

Now,

$\begin{array}{l} \sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} + \sqrt{\frac{c}{a}} \\ = \sqrt{\frac{α}{β}} + \sqrt{\frac{β}{α}} + \sqrt{\frac{c}{a}} \\ = \frac{α + β}{\sqrt{α β}} + \sqrt{\frac{c}{a}} \\ = \frac{- \frac{c}{a}}{\sqrt{\frac{c}{a}}} + \sqrt{\frac{c}{a}} \\ = - \sqrt{\frac{c}{a}} + \sqrt{\frac{c}{a}} \\ = 0 \end{array}$