• # question_answer The value of ?$c$?for which $|{{\alpha }^{2}}-{{\beta }^{2}}|=\frac{7}{4}$, where $\alpha$ and $\beta$ are the roots of $2{{x}^{2}}+7x+c=0$,  is A) 4 B) 0 C) 6 D) 2

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