If in the expansion of (1+p x)^ n , n N , the coefficient of x and x² are 8 and 24 , then

Step-by-step solution

We have, (1+p x)^ n T_ r+1 = n r (1)^ n-r (p x)^ r T_ r+1 = n r p^ r x^ r Coefficient of x^ r = n r p^ r Now, coefficient of x= n 1 p=8 (put r=1 ) n p=8 (i) Also, coefficient of x²= n 2 p²=24 (put .r=2 ) n(n-1) 2 p²=24 [from Eq.(i)] n(n-1) 2 ( 8 n )²=24 64(n-1) 2 n =24 4(n-1)=3 n n=4 From Eq. (i), we get p=2