Question

Let $x^2-(M-3)x+M=0;MϵR$ be a quadratic equation. If both the roots are greater than 2 then M lies in the interval

• A. $\varphi$
• B. $(3,\infty )$
• C. [9, 10)
• D. (3, 9]

Answer 1

The correct option is C [9, 10)

I $\Delta \ge 0\Rightarrow (M-3{)}^2-4M\ge 0\Rightarrow Mϵ(-\infty ,1]\cup [9,\infty )\to (1)$
II $f\left(2\right)>0\Rightarrow 4-(M-3)2+M>0\Rightarrow M<10\to \left(2\right)$
III $\frac{-b}{2a}>2\Rightarrow \frac{M-3}{2}>2\Rightarrow M>7\to \left(3\right)$
The intersection of (1) , (2) and (3) is $Mϵ[9,10)$