Question

If the roots of the equation $x^2-2ax+a^2+a-3=0$ are less than $3$ then

• A. $a<2$
• B. $2\le a\le 3$
• C. $3<a\le 4$
• D. $a>4$

Answer 1

The correct option is A $a<2$

Let $p$ and $q$ be the roots of the equation, then

$p+q=2a$

Also it is given that,

$p<3$ and $q<3$

So, $p+q<6$

$2a<6$

$a<3$

So, for any integral value of $p$ and $q$ less than $3$, value of $a$ is always less than $3$. Hence the soution set of $a$ will always be $(-\infty ,2)$