Question

If $1\in (\alpha ,\beta )$ where $\alpha ,\beta$ are the roots of the equation $x^2-a(x+1)+3=0$, then

• A. $a>2$
• B. $a<-6ora>2$
• C. $-6<a<2$
• D. $a<2$

Answer 1

Answer: (A)

$a>2$

Let $f\left(x\right)=x^2-a(x+1)+3$

If $1\in (\alpha ,\beta )$

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

$\Rightarrow 1-a\left(2\right)+3<0$

$\Rightarrow 4-2a<0\Rightarrow 2a-4>0$

$\Rightarrow a>\frac{4}{2}=2$