If (x¹⁰⁰ + 2x⁹⁹ + k) is divided by (x + 1), then the value of k is
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Answered by
8
Answer:
k = 1
Step-by-step explanation:
As (x¹⁰⁰ + 2x⁹⁹ + k) is divided by (x + 1), x + 1 is a factor of (x¹⁰⁰ + 2x⁹⁹ + k).
We know that if x + a is factor of P(x) then, P(-a) = 0
So, here P(x) = (x¹⁰⁰ + 2x⁹⁹ + k) and a = -1
So, substituting, we get
P(-1) = [(-1)¹⁰⁰ + 2(-1)⁹⁹ + k] = 0
=> 1 + 2(-1) + k = 0
=> 1 - 2 + k = 0
=> -1 + k = 0
=> k - 1 = 0
Hope it helps
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Answered by
1
Answer:
As (x¹⁰⁰ + 2x⁹⁹ + k) is divided by (x + 1), x + 1 is a factor of (x¹⁰⁰ + 2x⁹⁹ + k).
We know that if x + a is factor of P(x) then, P(-a) = 0
So, here P(x) = (x¹⁰⁰ + 2x⁹⁹ + k) and a = -1
So, substituting, we get
P(-1) = [(-1)¹⁰⁰ + 2(-1)⁹⁹ + k] = 0
=> 1 + 2(-1) + k = 0
=> 1 - 2 + k = 0
=> -1 + k = 0
=> k - 1 = 0
➡ K=1
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