If every pair of the equations $x^{2} + p x + q r = 0, x^{2} + q x + r p = 0, x^{2} + r x + p q = 0$ have a common root, then the sum of three common roots is

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Solution

The correct option is A

Let the roots be α, β; β, γ and γ, α respectively.

∴ α + β = -p, β + γ = -q, γ + α = -r

Adding all, we get ∑α = $\frac{- (p + q + r)}{2}$ etc.

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The correct option is A Let the roots be α, β; β, γ and γ, α respectively. ∴ α + β = -p, β + γ = -q, γ + α = -r Adding all, we get ∑α = −(p+q+r)2 etc.

If every pair of the equations $x^{2} + p x + q r = 0, x^{2} + q x + r p = 0, x^{2} + r x + p q = 0$ have a common root, then the sum of three common roots is

The correct option is A

Let the roots be α, β; β, γ and γ, α respectively.

∴ α + β = -p, β + γ = -q, γ + α = -r

Adding all, we get ∑α = $\frac{- (p + q + r)}{2}$ etc.