A) \[{{x}^{2}}+2x+15=0\]
B) \[{{x}^{2}}+15x+2=0\]
C) \[2{{x}^{2}}-2x+15=0\]
D) \[{{x}^{2}}-2x-15=0\]
Correct Answer: D
Solution :
Let roots are \[\alpha \] and \[\beta \] \[\alpha +\beta =2\]and \[{{\alpha }^{3}}+{{\beta }^{3}}=98\] \ \[{{\alpha }^{3}}+{{\beta }^{3}}=(\alpha +\beta )({{\alpha }^{2}}-\alpha \beta +{{\beta }^{2}})\] Þ \[98=2\left[ {{(\alpha +\beta )}^{2}}-3\alpha \beta \right]\Rightarrow 49=(4-3\alpha \beta )\] Þ \[\alpha \beta =-15\] Thus equation is \[{{x}^{2}}-2x-15=0\].
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