Let t denote the greatest integer ≤ t . if the constant term in the expansion of 3 x 2 - 1 2 x 5 7 is α then α is equal to _ _ _ _ _

Question

Let t denote the greatest integer &#8804; t . if the constant term in the expansion of 3 x 2 - 1 2 x 5 7 is &#945; then &#945; is equal to _ _ _ _ _

Quantrex Academy · Accepted Answer

Correct answer: 0

The given expansion is 3 x 2 - 1 2 x 5 7 . The general term in the binomial expansion of x + a n is given by T r + 1 = C r n x n - r a r . &#8658; T r + 1 = C r 7 3 x 2 7 - r - 1 2 x 5 r = C r 7 - 1 r 3 7 - r 2 r x 14 - 2 r - 5 r Now for term independent of x &#8658; 14 - 2 r - 5 r = 0 &#8658; r = 2 Coefficient of x 0 is C 2 7 - 1 2 &#215; 3 7 - 2 2 2 = 7 &#215; 6 2 &#215; 3 5 2 2 . &#8658; &#945; = 5103 4 &#8658; &#945; = 1275 Hence this is the required answer.

Let t denote the greatest integer ≤ t . if the constant term in the expansion of 3 x 2 - 1 2 x 5 7 is α then α is equal to _ _ _ _ _

Correct answer

Step-by-step solution

More from Binomial Theorem

Let t denote the greatest integer &#8804; t . if the constant term in the expansion of 3 x 2 - 1 2 x 5 7 is &#945; then &#945; is equal to _ _ _ _ _

Correct answer

Step-by-step solution

More from Binomial Theorem

Let t denote the greatest integer ≤ t . if the constant term in the expansion of 3 x 2 - 1 2 x 5 7 is α then α is equal to _ _ _ _ _