A) 2
B) 3
C) 6
D) 5
Correct Answer: C
Solution :
| \[|{{\alpha }^{2}}-{{\beta }^{2}}=\,\,|(\alpha +\beta )|\,\,\,|\alpha -\beta |\] |
| \[\Rightarrow \,\,\,\frac{7}{4}=|\alpha -\beta |.\frac{7}{2}\] |
| \[\Rightarrow \,\,\,|\alpha -\beta {{|}^{2}}=\frac{1}{4}\,\,\,\Rightarrow \,\,\,|{{(\alpha +\beta )}^{2}}-4\alpha \beta |=\frac{1}{4}\] |
| \[\Rightarrow \,\,\left| \frac{49}{4}-\frac{4c}{2} \right|=\frac{1}{4}\] |
| \[\Rightarrow \,\,49-8c=1\Rightarrow \,c=\frac{48}{8}=6\] |
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