Question

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

• A. $\left(-\infty ,2\right)$
• B. $\left(-\infty ,\frac{9}{4}\right)$
• C. $\left(2,\frac{\theta }{4}\right)$
• D. $\left(3,\frac{\theta }{4}\right)$

Answer 1

The correct option is B $\left(-\infty ,\frac{9}{4}\right)$

solution : -

Given $x_1$ and $x_2$ are the roots of $x^2-3x+a=0$

$aϵR$ and $x_1<1<x_2$ then we $A{x}^2+Bx+c=0$

Hence $A=1,B=-3,C=a$

then $D=B^2-4AC=9-4\left(1\right)\left(a\right)=9-4a$

$9-4a\ge 0$

$\Rightarrow 4a\le 9$

$\Rightarrow a\le \frac{9}{4}$

$aϵ(-\infty ,\frac{9}{4})$