Question

If the difference of the roots is equal to the product of the roots of the equation $2x^2-(a+1)x+(a-1)=0$ then the value of a is?

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A $2$

$2x^2-(a+1)x+(a-1)=0$

let two roots be $\alpha ,\beta$ By trial and error we can say that 1 is the one of the root so let $\beta =1$

$\therefore \alpha -\beta =\alpha \beta$

$\Rightarrow \sqrt{(\alpha +\beta {)}^2-4\alpha \beta }=\alpha \beta$

$\Rightarrow \sqrt{{\left(\frac{a+1}{2}\right)}^2-4\frac{(a-1)}{2}}=\frac{a-1}{2}$

$\Rightarrow \sqrt{\frac{a^2+2a+1}{4}-2(a-1)}=\frac{a-1}{2}$

$\Rightarrow \frac{a^2+2a+1-8a+8}{4}=\frac{a^2-2a+1}{4}$

$\Rightarrow -4a+8=0$

$\Rightarrow a=2$