99 Percentile Qs Bank for JEE MainMathematicsQuadratic Equation
The remainder obtained by dividing the polynomial x 100 by the polynomial x 2 - 3x + 2 is equal to
Options
- A2 100 - 1
- B(2 100 - 1) x - 2 (2 99 - 1)
- C2 100 x - 3.2 100
- D(2 100 - 1) x + 2 (2 99 - 1)
Correct answer
B. (2 100 - 1) x - 2 (2 99 - 1)
Step-by-step solution
Concept Involved Remainder Theorem If a polynomial P(x) is divided by x - α , then the remainder obtained is equal to p α . Dividend x 100 Divisor x 2 - 3x + 2 = (x - 1) (x - 2) Let P(x) = x 100 = (x - 1) (x - 2) Q(x) + R(x) ...(i) Since, the divisor is a quadratic, hence the degree of remainder should be less than 2 (i.e., ≤ 1). Let us assume that the remainder obtained is R(x) = ax + b, then to find R(x), we have to basically find the values of a and b. On substituting x = 1 in Eq. (i) we get P(1)