Question

Let $S$ be the set of all possible integral values of $\lambda$ in the interval $(-3,7)$ for which the roots of the quadratic equation $\lambda x^{2}+13 x+7=0$ are all rational numbers. Then the sum of the elements in $S$ is

• A. 4
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (A)

We have
$\lambda x^{2}+13 x+7=0 $
$\therefore D=(13)^{2}-4(\lambda)(7)=169-28 \lambda$
For rational roots, $D=$ perfect square
So, $\lambda \in(-3,7)$ has values $-2,0,6$
so that $D$ become perfect square.
$\therefore $ Required sum $=-2+0+6=4$