Find the term independent of x 4 + x + 7x2 x - 3x11 - Maths - Binomial Theorem

Question

Find the term independent of x

4   +   x   +   7 x 2   x   -  
3 x 11

Lovina Kansal · Accepted Answer

Dear student
Given expansion is 4+x+7x2x-3x11Now, consider x-3x11Tr+1=11Crx11-r-3xr=11Crx11-r-3r1xr=11Crx11-2r-3rHence, the general term in the expansion of 4+x+7x2x-3x11=411Crx11-2r-3r+11Crx12-2r-3r+711Crx13-2r-3rFor term independent of x,putting 11-2r=0,12-2r=0 and 13-2r=0,we getr=112,r=6 and r=132Since, the possible value of r=6
Hence, first term and third term is not independent of x
∴The term independent of x is 11C6x12-12-36=11!6! 5!×-36  =11×10×9×8×7×6!6!×5×4×3×2=462
Regards

Find the term independent of x 4 + x + 7 x 2 x - 3 x 11

Find the term independent of x

$(4 + x + 7 x^{2}) {(x - \frac{3}{x})}^{11}$