Complex Numbers And Quadratic Equations

Question
CBSEENMA11015698

The sum of the coefficients of all odd degree terms in the expansion of x + x3 -15 + x - x3-15, (x>1) is

  • 2

  • -1

  • 0

  • 1

Solution

A.

2

x  + x3 -15 + x  -x3 -15 =2 [C02x5 + C25 x3 (x3-1) + C45 x (x3-1)2] = 2 [x5 + 10 (x6 - x3) + 5x(x6-2x3 +1)] = 2[ x5 + 10x6 - 10x3 + 5x7 -10x4 + 5x]= 2[5x7 + 10x6 + x5 - 10x4-10x3 + 5x]

Sum of odd degree terms coefficients
= 2(5 + 1 – 10 + 5)
= 2

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