If \( \Large \left(x+1\right) \) is a factor of \( \Large x^{4}+9x^{3}+7x^{2}+9ax+5a^{2} \), then
Correct Answer: |
B) \( \Large 5a^{2}-9a-1=0 \) |
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Description for Correct answer:
By factor theorem, if \( \Large x+1 \) is a factor of \( \Large p \left(x\right) \), then \( \Large p \left(-1\right)=0 \)
Therefore, \( \Large p \left(-1\right)= \left(-1\right)^{4}+9 \left(-1\right)^{3}+7 \left(-1\right)^{2}+9a \left(-1\right)+5a^{2} \)
= \( \Large 1-9+7-9a+5a^{2} = 5a^{2}-9a-1 \)
Therefore, \( \Large 5a^{2}-9a-1 = 0 \)
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