First slide

Theory of equations

Question

If the equation $x^{2} + p x + q = 0 and x^{2} + qx + p = 0$ , have a common root, then $p + q + 1 =$

Moderate

A

0
B

1
C

$2$
D

$- 1$

Solution

Let $α$ is the common root, so $α^{2} + pα + q = 0 . . . (i)$
and $α^{2} + qα + p = 0 . . . (ii)$
from $(i) - (ii)$ ,
$(a - b) α + 20 = 0$
$\Rightarrow (p - q) α + (q - p) = 0 \Rightarrow α = 1$
Put the value of $α$ in (i), $p + q + 1 = 0 .$

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