If every pair from among the equations $x^{2} + p x + q r = 0$ , $x^{2} + q x + r p = 0$ , and $x^{2} + r x + p q = 0$ has a common root, then the product of three common roots is

p q r

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2 p q r

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p^{2} q^{2} r^{2}

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p + q + r

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Solution

The correct option is B $p q r$
Let $(α, β), (β, γ), (γ, α)$ be the roots of the given three equations .
$\Rightarrow α β = q r; β γ = r p; γ α = p q$
Multiplying these equations we get
$α^{2} β^{2} γ^{2} = p^{2} q^{2} r^{2}$
$\Rightarrow α β γ = p q r$

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The correct option is B $p q r$
Let $(α, β), (β, γ), (γ, α)$ be the roots of the given three equations .
$\Rightarrow α β = q r; β γ = r p; γ α = p q$
Multiplying these equations we get
$α^{2} β^{2} γ^{2} = p^{2} q^{2} r^{2}$
$\Rightarrow α β γ = p q r$