The remainder, when x200 is divided by x2 – 3x + 2 is(a) (2200 – 1

1.	The remainder, when x200 is divided by x2 – 3x + 2 is(a) (2200 – 1) x + (–2200 + 2) (b) (2200 + 1) x + (–2200 – 2) (c) (2200 – 1) x + (–2200 – 2) (d) 2100
Answer» (a) (2²⁰⁰ – 1) x + (–2²⁰⁰ + 2) Let x²⁰⁰ = (x² – 3x + 2). Q(x) + lx + m ...(i) where, Q(x) = quotient and (lx + m) is the remainder Now (x² – 3x + 2) = 0 ⇒ (x – 1) (x – 2) = 0 ⇒ x = 1, 2. Substituting x = 1 in (i), we have, 1²⁰⁰ = 0. Q.(x) + l + m ...(ii) Similarly, for x = 2, 2²⁰⁰ = 0. Q(x) + 2l + m ...(iii) ∴ l + m = 1, 2l + m = 2²⁰⁰ Solving we get, l = 2²⁰⁰ – 1 and m = 2 – 2²⁰⁰ Hence remainder = lx + m = (2²⁰⁰ – 1) x + (–2²⁰⁰ + 2).

The remainder, when x200 is divided by x2 – 3x + 2 is(a) (2200 – 1) x + (–2200 + 2) (b) (2200 + 1) x + (–2200 – 2) (c) (2200 – 1) x + (–2200 – 2) (d) 2100

Answer»

(a) (2²⁰⁰ – 1) x + (–2²⁰⁰ + 2)

Let x²⁰⁰ = (x² – 3x + 2). Q(x) + lx + m ...(i)

where, Q(x) = quotient and (lx + m) is the remainder

Now (x² – 3x + 2) = 0 ⇒ (x – 1) (x – 2) = 0 ⇒ x = 1, 2.

Substituting x = 1 in (i), we have,

1²⁰⁰ = 0. Q.(x) + l + m ...(ii)

Similarly, for x = 2,

2²⁰⁰ = 0. Q(x) + 2l + m ...(iii)

∴ l + m = 1, 2l + m = 2²⁰⁰

Solving we get, l = 2²⁰⁰ – 1 and m = 2 – 2²⁰⁰

Hence remainder = lx + m = (2²⁰⁰ – 1) x + (–2²⁰⁰ + 2).