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### Show Tags

29 Jan 2019, 08:13
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

40% (02:46) correct 60% (02:13) wrong based on 16 sessions

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If $$P(x)$$ be a polynomial satisfying the identity $$P(x^{2}) +2x^{2} +10x = 2x\ P( x+1) +3$$, then $$P(x)$$ is
A) $$2x+3$$
B) $$3x-4$$
C) $$3x+2$$
D) $$2x–3$$
E) $$3x–3$$

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If P(x) be a polynomial satisfying the identity $P(x^{2}) +2x^{2} +10x [#permalink] ### Show Tags 29 Jan 2019, 08:51 2 P(x) = ax + b => P(x+1) = a(x+1) + b P(x^2) + 2x^2 + 10x = ax^2 + b + 2x^2 + 10x 2x*P(x+1) + 3 = 2x*[a(x+1) +b] + 3 P(x^2) + 2x^2 + 10x = 2x*P(x+1) + 3 <=> ax^2 + b + 2x^2 + 10x = 2x*[a(x+1) +b] + 3 <=> (a+2)*x^2 + 10x + b = 2a*x^2+ 2ax + 2bx + 3 <=> (a+2) * x^2 + 10x + b = 2a *x^2 + (2a+2b)*x + 3 we have a+2 = 2a => a=2 b is found by 2 ways: b=3 or 10 = 2a + 2b => b = (10-2*2)/2 = 3 => P(x) = 2x + 3 A If P(x) be a polynomial satisfying the identity$P(x^{2}) +2x^{2} +10x   [#permalink] 29 Jan 2019, 08:51
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# If P(x) be a polynomial satisfying the identity \$P(x^{2}) +2x^{2} +10x

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