Question

If $a$ and $b$ are the roots of $x^2-px+q=0$, then $a^2+b^2$ is

• A. $p^2+q^2$
• B. $p^2+2q$
• C. $p^2-q^2$
• D. $p^2-2q$

Answer 1

The correct option is D $p^2-2q$

Given quadratic equation is $x^2-px+q=0$

For the quadratic equation $a{x}^2+x+c=0$,

the sum of the roots is $\frac{-b}{a}$ and product of the roots is $\frac{c}{a}$

Here the roots of the given equation are $a$ and $b$.

$a^2+b^2=(a+b{)}^2-2ab$

$=p^2-2q$

Therefore,Option D is correct.