Question

If both roots of the quadratic equation $x^2-2x+a-3=0$ are positive and distinct then value of $a$ is

• A. $(0,1)$
• B. $(1,2)$
• C. $(2,3)$
• D. $(3,4)$

Answer 1

Answer: (D)

$D>0\Rightarrow 4-4(a-3)>0\Rightarrow a<4$
$\text{ Sum }>0\Rightarrow 2>0$
$\text{ Product }>0\Rightarrow a-3>0\Rightarrow a>3$
$\therefore a\in (3,4)$