| If \[{{x}^{2}}-x-12=0,\]then the value of \[[{{x}^{5}}-13{{x}^{3}}-11{{x}^{2}}-x-12]\] is |
A) 0
B) 1
C) 2
D) 3
Correct Answer: A
Solution :
| \[{{x}^{2}}-x-12=0\] |
| On dividing \[{{x}^{5}}-13{{x}^{3}}-11{{x}^{2}}-x-12\]by \[{{x}^{2}}-x-12,\]we get |
| \[{{x}^{5}}-13{{x}^{3}}-11{{x}^{2}}-x-12=({{x}^{2}}-x-12)({{x}^{3}}+{{x}^{2}}+1)\] \[=0\times ({{x}^{3}}+{{x}^{2}}+11)=0\] |
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