Question

If Q(x) is the quotient when P(x) = 1111x¹¹¹¹ – 111x¹¹¹ + 11x¹¹ – 1011 is divided by x – 1, then sum of the digits in the sum of coefficients of Q(x) is ______.

Options

• 11.0

• 12.00

• 13.0

• 14.0

Answer 1

If Q(x) is the quotient when P(x) = 1111x¹¹¹¹ – 111x¹¹¹ + 11x¹¹ – 1011 is divided by x – 1, then sum of the digits in the sum of coefficients of Q(x) is 11.0.

Explanation:

Q(x) is equivalent to  `("df")_(x→1) (1111x^(1111) - 111x^(111) + 11x^(11) - 1011)/(x - 1)`

= 1111² – 111² + 11²

= (1111 – 111)(1111 + 111) + 121

= 1222121

∴ Sum of digits = 11.