If every pair among the equations $x^{2} + p x + q r = 0, x^{2} + q x + r p = 0$ and $x^{2} + r x + p q = 0$ have a common root, then $\frac{(s u m o f r o o t s)}{(p r o d u c t o f r o o t s)}$ =

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Solution

The correct option is C

$x^{2} + q x + r p = 0$ ; $α, β$

$x^{2} + p x + r q = 0$ ; $β, γ$

$x^{2} + r x + p q = 0$ ; $γ, α$

Then, $β^{2} + q β + r p = 0, β^{2} + p β + q r = 0$

$\Rightarrow (q - p) β$ = r(q-p) $\Rightarrow$ $β$ = r.

Similarly , $γ = q, α = p$ .

$∴$ $\frac{(α + β + γ)}{α β γ}$ = $\frac{(p + q + r)}{p q r}$ .

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