Question

Find the value of $m$ such that roots of the quadratic equation $x^2-(m-3)x+m=0$ $(m\in R)$ are not real

• A. $(-1,-9)$
• B. $(-\infty ,1)$
• C. $(9,\infty )$
• D. $(1,9)$

Answer 1

The correct option is D $(1,9)$

Condition for not real (imaginary) roots:
$D<0$
$\Rightarrow (m-3{)}^2-4m<0$
$\Rightarrow m^2-6m+9-4m<0$
$\Rightarrow m^2-10m+9<0$
$\Rightarrow (m-1)(m-9)<0$

Hence, $m\in (1,9)$