Question

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

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (D)

$2$

Let $\alpha ,\beta$ be the roots of $2x^2-(a+1)x+(a-1)=0$
$\alpha -\beta =\alpha \beta$
$\Rightarrow \frac{\sqrt{D}}{A}=\frac{C}{A}$
$\Rightarrow B^2-4AC=C^2$
$\Rightarrow (a+1{)}^2-8(a-1)=(a-1{)}^2$
$\Rightarrow 4a=8(a-1)$
$\therefore a=2$
Hence, option D.