Question

If $x_1,x_2$ are the roots of $x^2-3x+a=0,a\in R$ and $x_1<1<x_2$

• A. $(-\infty ,2)$
• B. $(-\infty ,9/4)$
• C. $(2,9/4)$
• D. none of these

Answer 1

The correct option is A $(-\infty ,2)$

$x^2-3x+a=0$

This expression will have an upward parabola graph cuttiing $x$ axis on either sides of $x=1$

$f\left(1\right)<0$

$\Rightarrow 1-3+a<0$

$\Rightarrow -2+a<0$

$\Rightarrow a<2$

$\therefore a\in (-\infty ,2)$