Question

The value of $c$ for which $|{\alpha }^2-{\beta }^2|=\frac{7}{4}$ , where $\alpha$ and $\beta$ are the roots of $2x^2+7x+c=0$ , is

• A. 6
• B. 2
• C. 4
• D. 0

Answer 1

The correct option is A

6

We have $\alpha +\beta =\frac{7}{2}and\alpha \beta =\frac{c}{2}$

$\therefore |{\alpha }^2-{\beta }^2|=\frac{7}{4}\Rightarrow {\alpha }^2-{\beta }^2=\pm \frac{7}{4}\Rightarrow (\alpha +\beta )(\alpha -\beta )=\pm \frac{7}{4}\Rightarrow -\frac{7}{2}\sqrt{\frac{49}{4}-2c}=\pm \frac{7}{4}\Rightarrow \sqrt{49-8c}=\mp 1\Rightarrow 49-8c=1\Rightarrow c=6$