The value of p and q (P 0, q 0) for which p, q are the roots of t… - Vidyadip

MCQ

The value of p and q $(\text{P}\neq0,\ \text{q}\neq0)$ for which p, q are the roots of the equation $x^2 + px + q = 0$ are:

✓
p = 1, q = −2
B
p = −1, q = −2
C
p = −1, q = 2
D
p = 1, q = 2

✓

Answer

Correct option: A.

p = 1, q = −2

p = 1, q = −2

Solution:
It is given that, p and q $(\text{P}\neq0,\ \text{q}\neq0)$are the roots of the equation $x2 + px + q = 0$
$\therefore \text { Sum of roots }=p+q=-p$
$\Rightarrow 2 p+q=0 \ldots(1)$
$\text { Product of roots }=p q=q$
$\Rightarrow q(p-1)=0$
$\Rightarrow p=1, q=0$
Now, substituting $p=1$ in (1), we get,
$2+q=0$
$\Rightarrow q=-2$

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