A) \[{{x}^{3}}+7x-6\]
B) \[{{x}^{3}}+7x+6\]
C) \[{{x}^{3}}-7x-6\]
D) \[{{x}^{3}}-7x+6\]
Correct Answer: D
Solution :
| [d] Let \[\alpha ,\beta ,\gamma \] be the zeroes of the required polynomials |
| \[\alpha +\beta +\gamma =0\] |
| \[\alpha \beta +\beta \gamma +\alpha \gamma =-7\] |
| \[\alpha \beta \gamma =-6\] |
| Required cubic polynomial is |
| \[k[{{x}^{3}}-(\alpha +\beta +\gamma ){{x}^{2}}+\] |
| \[(\alpha \beta +\beta \gamma +\gamma \alpha )x-\alpha \beta \gamma ]\] |
| where k is non-zero constant |
| \[k[{{x}^{3}}+(0){{x}^{2}}+(-7)x-(-6)]={{x}^{3}}-7x+6\] |
| [consider, \[k=1\]] |
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