Question

$x^2-(m-3)x+m=0(m\in R)$ be a quadratic equation. Find the value of $m$ for which both the roots are greater than $2$

• A. $(9,10)$
• B. $(-5,4)$
• C. $(6,\infty )$
• D. None of the above.

Answer 1

The correct option is A $(9,10)$

First there exists 2 roots $\Rightarrow (m-3{)}^2>4m$

$\Rightarrow (m-1)(m-9)>0$

$\therefore m\in (-\infty ,1)\cup (9,\infty )$

And both roots are greater than 2 $\Rightarrow$f(2)>0

$\Rightarrow 10-m>0$

$\Rightarrow m<10$

Combining both we get $m\in (9,10)$