Engineering
Mathematics
Introduction to Binomial Theorem
Application of Binomial Theorem and Summation Of Series
Question
If the coefficient of x2 and x3 are both zero, in the expansion of the expression (1 + ax + bx2) (1 – 3x)15 in powers of x, then the ordered pair (a, b) is equal to
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Solution
Coefficient of x2 = 15C2 × 9 – 3a (15C1) + b = 0
⇒ 15C2 × 9 – 45a + b = 0 (1)
Coefficient of x2 = –27 × 15C3 + 9a × 15C2 –3b × 15C1 = 0
⇒ –273 + 21a – b = 0 (2)
(1) + (2) give
–24a + 672 = 0 ⇒ a = 28, b = 315