First slide

Theory of equations

Question

If every pair of the equations $x^{2} + px + qr = 0, x^{2} + qx + rp = 0, x^{2} + rx + pq = 0$
have a common root, then the sum of three common roots is

Moderate

A

$\frac{- (p + q + r)}{2}$
B

$\frac{- p + q + r}{2}$
C

$- (p + q + r)$
D

$- p + q + r$

Solution

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 $\sum_{} α = - (p + q + r) / 2 etc .$

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