Question

Find the value of $m$ such that roots of the quadratic equation $x^2-(m-3)x+m=0$ $(m\in R)$ are equal in magnitude but opposite in sign.

• A. $\varphi$
• B. $(1,3)$
• C. None of the above.
• D. $(3,9)$

Answer 1

The correct option is A $\varphi$

Condition : when root are equal in magnitude but opposite in sign,

(i) $D>0$ (ii) Sum of roots $=0$

(i) $D>0$

$\Rightarrow (m-3{)}^2-4m>0$

$\Rightarrow m^2-6m+9-4m>0$

$\Rightarrow m^2-10m+9>0$

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

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

(ii) Sum of roots $=0$

$\Rightarrow$ Sum of roots $=(m-3)=0\Rightarrow m=3$

Now, taking intersection of both the condition, we get

$m\in \varphi$