11 th question please help
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NeelamG:
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Answered by
11
Answer:
Option(D)
Step-by-step explanation:
Given: f(x) = x²⁰⁰ - 2x¹⁹⁹ + x⁵⁰ - 2x⁴⁹ + x² + x + 1
By Division algorithm, we get
⇒ x²⁰⁰ - 2x¹⁹⁹ + x⁵⁰ - 2x⁴⁹ + x² + x + 1 + Ax + B
Given that f(x) is divided by (x - 1)(x - 2).
(i) When x = 1:
1 - 2 + 1 - 2 + 1 + 1 + 1 + A + B
1 = A + B
(ii) When x = 2:
2²⁰⁰ - 2²⁰⁰ + 2⁵⁰ - 2⁵⁰ + 4 + 2 + 1
7 = 2A + B
On solving (i) & (ii), we get
A + B = 1
2A + B = 7
------------------
A = 6
Substitute A = 6 in (i), we get
⇒ A + B = 1
⇒ 6 + B = 1
⇒ B = -5
∴ Remainder = 6x - 5
Hope it helps!
Answered by
5
P(x) / a quadratic ----> remainder = ax + b , with a , b constant
remainder theorem ---> P(1) = .... = 1 = a+b
and P(2) = ... = 7 = 2a + b
solve 2 equations for a , b
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