Question

Let $x^2-(m-3)x+m=0,m\in R$ be a quadratic equation. Then the set of value(s) of $m$ for which roots are real and distinct is/are

• A. $(-\infty ,1)$
• B. $(1,9)$
• C. $(9,\infty )$
• D. $\left\{1\right\}$

Answer 1

Answer: (A), (C)

The correct options are
A $(-\infty ,1)$
C $(9,\infty )$

$x^2-(m-3)x+m=0$
Roots are real and distinct.
$\therefore D>0\Rightarrow (m-3{)}^2-4m>0\Rightarrow m^2-6m+9-4m>0\Rightarrow m^2-10m+9>0\Rightarrow (m-1\left)\right(m-9)>0\therefore m\in (-\infty ,1)\cup (9,\infty )$