Question

Find the value of $m$ such that at least one root of the quadratic equation $x^2-(m-3)x+m=0$ $(m\in R)$ lies in the interval $(1,2)$

• A. $\varphi$
• B. $[9,\infty )$
• C. $(-\infty ,1]$
• D. $(10,\infty )$

Answer 1

The correct option is D $(10,\infty )$

When exactly one root lies in the interval $(1,2)$ then $m\in (10,\infty )$

And, when both roots lies in the interval $(1,2)$ then $m\in \varphi$

Upon taking union of both the cases, we get

$m\in (10,\infty )$