If a b 0 and the sum of the coefficients of x^7 and x^4 in the expansion of ( x^2 a - b x )¹¹ is 0 , then

Step-by-step solution

Given expansion is ( x^2 a - b x )¹¹ . The general term is aligned T_ r+1 & ¹¹ C_r ( x^2 a )^ 11-r (- b x )^r & = ¹¹ C_r(x)^ 22-3 r (-b)^r ( 1 a )^ 11-r aligned For coefficient x^7 , put 22-3 r=7 aligned & & 3 r & =15 & & r & =5 aligned and for coefficient of x^4 , put 22-3 r=4 aligned & 3 r=18 r=6 & T₆= ¹¹ C₅ ( 1 a )^6(-b)^5 & and T₇= ¹¹ C₆ ( 1 a )^6(-b)^6 aligned According to the given condition, array rlrl & ^ T₆ +T₇=0 & ¹¹ C₅ ( 1 a )^6(-b)^5+ ¹¹ C₆ ( 1 a )^5(-b)^6=0 & ¹¹ C₅ ( 1 a )^5(-b)^5 ( 1 a -b )=0 & & 1 a