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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
Options:
$x^2+p x+q r=0, x^2+q x+r p=0, x^2+r x+p q=0$
have a common root, then the sum of three common roots is
Solution:
2998 Upvotes
Verified Answer
The correct answer is:
$\frac{-(p+q+r)}{2}$
Let the roots be $\alpha, \beta ; \beta, \gamma$ and $\gamma, \alpha$ respectively.
$\therefore \quad \alpha+\beta=-p, \beta+\gamma=-q, \gamma+\alpha=-r$
Adding all, we get $\Sigma \alpha=-(p+q+r) / 2$ etc.
$\therefore \quad \alpha+\beta=-p, \beta+\gamma=-q, \gamma+\alpha=-r$
Adding all, we get $\Sigma \alpha=-(p+q+r) / 2$ etc.
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