Let p x 4 + q x 3 + r x 2 + s x + t = x 2 + 3 x x - 1 x + 3 x + 1 - 2 x x - 4 x - 3 x + 4 3 x be an identity, where p ,   q ,   r ,   s and t are constants, then the value of s is equal to

Step-by-step solution

Differentiating both sides, we get, 4 p x 3 + 3 q x 2 + 2 x r + s = 2 x + 3 1 1 x + 1 - 2 x x - 4 x - 3 x + 4 3 x + x 2 + 3 x x - 1 x + 3 1 - 2 1 x - 3 x + 4 3 x + x 2 + 3 x x - 1 x + 3 x + 1 - 2 x x - 4 1 1 3 Putting x = 0 , we get, s = 3 1 1 1 0 - 4 - 3 4 0 + 0 - 1 3 1 - 2 1 - 3 4 0 + 0 - 1 3 1 0 - 4 1 1 3 s = 64 - 3 + 10 = 7 1