Question

$x^2-(m-3)x+m=0(m\in R)$ be a quadratic equation. Find the value of $m$ for which, one root is smaller than $2$. The other root is greater than $2$.

• A. $(-\infty ,1]$
• B. $(-3,12)$
• C. $(10,\infty )$
• D. None of the above.

Answer 1

Answer: (C)

$(10,\infty )$

One root is greater than 2 and other root is less than 2

Analyse the diagram of that parabola

We see that f(2)<0

$\Rightarrow 4-2(m-3)+m<0$

$\Rightarrow m-10>0$

$\Rightarrow m>10$

$\Rightarrow m\in (10,\infty )$