Question

The range of a such that the quadratic equation $x^2+(a-3)x+a=0$ has two distinct positive roots, is

• A. $(0,\infty )$
• B. $(0,1)$
• C. $(-\infty ,1)$
• D. $(9,\infty )$

Answer 1

Answer: (B)

$D>0\Rightarrow (a-3{)}^2-4a>0\Rightarrow a^2-10a+9>0\Rightarrow (a-9)(a-1)>0\dots \dots ..(1)$
$\frac{-b}{2a}>0\Rightarrow \frac{3-a}{2}>0\Rightarrow a<3$ .....(2)
and product of the roots $>0\Rightarrow a>0\dots ..$. (3)
$(1),(2)$ and $(3)\Rightarrow a\in (0,1)$