Question:
The value of $p$ and $q(p \neq 0, q \neq 0)$ for which $p, q$ are the roots of the equation $x^{2}+p x+q=0$ are
(a) p = 1, q = −2
(b) p = −1, q = −2
(c) p = −1, q = 2
(d) p = 1, q = 2
Solution:
(a) p = 1, q = −2
It is given that, $p$ and $q(p \neq 0, q \neq 0)$ are the roots of the equation $x^{2}+p x+q=0$.
$\therefore$ Sum of roots $=p+q=-p$
$\Rightarrow 2 p+q=0 \quad \ldots(1)$
Product of roots $=p q=q$
$\Rightarrow q(p-1)=0$
$\Rightarrow p=1, q=0$ but $q \neq 0$
Now, substituting p = 1 in (1), we get,
$2+q=0$
$\Rightarrow q=-2$
Disclaimer: The solution given in the book is incorrect. The solution here is created according to the question given in the book.