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  4. If both roots of the quadratic equation x2-2 x+a-3=0 are positive and distinct then value of a is

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

Complex Numbers and Quadratic Equations

Solution:

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