A) \[{{x}^{2}}+14x+74=0\]
B) \[{{x}^{2}}-14x-74=0\]
C) \[{{x}^{2}}+14x-74=0\]
D) \[{{x}^{2}}-14x+74=0\]
Correct Answer: D
Solution :
First root, \[\alpha =7+5i\] Let second root \[\beta =7-5i\] \[\therefore \] \[\alpha +\beta =7+5i+7-5i=14\] \[\alpha .\beta =(7+5i)(7-5i)\] \[=49+25\] \[=74\] Hence, quadratic equation whose roots are\[\alpha \] and\[\beta \]is \[{{x}^{2}}-(\alpha -\beta )x+\alpha \beta =0\] \[\Rightarrow \] \[{{x}^{2}}-14x+74=0\]
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