A) 4
B) 0
C) 6
D) 2
Correct Answer: C
Solution :
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 \[\sqrt{49-8c}=\mp 1\,\,\Rightarrow \,49-8c=1\,\Rightarrow c=6\]
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