A) \[{{x}^{3}}+2{{x}^{2}}-5x-6\]
B) \[{{x}^{3}}+2{{x}^{2}}-5x+6\]
C) \[{{x}^{3}}+2{{x}^{2}}+5x-6\]
D) \[{{x}^{3}}+2{{x}^{2}}+5x+6\]
Correct Answer: A
Solution :
| Since, given polynomial has three zeroes. |
| So, it will be a cubic polynomial. |
| Now, sum of zeroes \[=-3-1+2=-2\] |
| Sum of product of two zeroes at a time |
| \[=-3\times \left( -1 \right)+\left( -1 \right)\times 2+2\times \left( -3 \right)\] |
| \[=3-2-6\] |
| \[=-5\] |
| and product of all zeroes \[=-3\times -1\times 2=6\] |
| \[\therefore \] Required cubic polynomial |
| \[={{x}^{3}}-\] (Sum of zeroes) \[{{x}^{2}}\] |
| + (Sum of product of two zeroes at a time) x - (Product of three zeroes) |
| \[={{x}^{3}}-\left( -2 \right){{x}^{2}}+\left( -5 \right)x-\left( 6 \right)\] |
| \[={{x}^{3}}+2{{x}^{2}}-5x-6\] |
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