Binomial-theorem-Given-that-the-coefficient-of-x-2-in-the-expansion-of-1-ax-3-2-x-5-is-1440-what-is-the-value-of-the-constant-a- Tinku Tara June 3, 2023 Permutation and Combination 0 Comments FacebookTweetPin Question Number 134798 by bramlexs22 last updated on 07/Mar/21 BinomialtheoremGiven that the coefficient of x^2 in the expansion of (1+ax) (3-2 x) ^5 is 1440, what is the value of the constant a? Answered by Ñï= last updated on 07/Mar/21 (52)(−2x)233+ax(51)(−2x)34=10(108−81a)x210(108−81a)=1440⇒a=−49 Answered by liberty last updated on 07/Mar/21 Wecanfindthecoefficientofx2forf(x)=(1+ax)(3−2x)5bytakingf″(0)2!(∙)f(x)=(1+ax)(3−2x)5f′(x)=a(3−2x)5−10(1+ax)(3−2x)4f′(x)=(3−2x)4[3a−2ax−10−10ax]f′(x)=(3−2x)4(−12ax+3a−10)(∙∙)f″(x)=−12a(3−2x)4−8(3−2x)3(−12ax+3a−10)f″(0)=−12a(81)−8(27)(3a−10)f″(0)2!=−6a(81)−4(27)(3a−10)=1440−486a−324a+1080=1440−810a=2520;a=−360810=−49 Answered by mr W last updated on 07/Mar/21 (1+ax)(3−2x)5=(1+ax)∑5k=0Ck535−k(−2x)k=(1+ax)∑5k=0Ck535−k(−2)kxkcoef.ofx2:C2535−2(−2)2+aC1535−1(−2)1=1080−810a=1440⇒a=−49 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: 2-4-x-2x-3-dx-Next Next post: Question-134801 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.