First slide

Theory of equations

Question

If $p, q$ are roots of $x^{2} + p x + q = 0,$ then

Easy

A

$p = 1$
B

$p = 1 o r 0$
C

$p = - 2$
D

$p = - 2 o r 0$

Solution

We have $p + q = - p, p q = q$
As $p q = q,$
we get $q (p - 1) = 0$
$\Rightarrow$ $q = 0 o r p = 1$
If $q = 0,$ we get $p = 0$
If $p = 1,$ we get $p + q = - p \Rightarrow q = - 2 .$
Thus, $p = 1$ or $p = 0 .$

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