If p and q are the roots of the equation x2 − px + q = 0, then

Question:

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

(a) $p=1, q=-2$

(b) $b=0, q=1$

(c) $p=-2, q=0$

(d) $p=-2, q=1$

Solution:

Given that $\rho$ and $q$ be the roots of the equation $x^{2}-p x+q=0$

Then find the value of $p$ and $q$.

Here, $a=1, b=-p$ and, $c=q$

p and be the roots of the given equation

Therefore, sum of the roots

$p+q=\frac{-b}{a}$

$=\frac{-p}{1}$

$=-p$

$q=-p-p$......(1)

$=-2 p$

Product of the roots

$p \times q=\frac{q}{1}$

As we know that

$p=\frac{q}{q}$

$=1$

Putting the value of $p=1$ in equation (1)

$q=-2 \times 1$

$=-2$

Therefore, the value of $p=1 ; q=-2$

Thus, the correct answer is (a)

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