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JEE Mains · Maths · STD 12 - 1. relation and function
If \(f(x)\) and \(g(x)\) are two polynomials such that the polynomial \(P ( x )=f\left( x ^{3}\right)+ xg \left( x ^{3}\right)\) is divisible by \(x^{2}+x+1,\) then \(P(1)\) is equal to ....... .
- A \(10\)
- B \(4\)
- C \(7\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\(P(x)=f\left(x^{3}\right)+\operatorname{xg}\left(x^{3}\right)\) \(P (1)=f(1)+ g (1) .....(1)\) Now \(P ( x )\) is divisible by \(x ^{2}+ x +1\) \(\Rightarrow P ( x )= Q ( x )\left( x ^{2}+ x +1\right)\) \(P ( w )=0= P \left( w ^{2}\right)\) where \(w , w ^{2}\) are non-real…
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