Math, asked by hanaa5038, 1 month ago

If (x¹⁰⁰ + 2x⁹⁹ + k) is divided by (x + 1), then the value of k is

Answers

Answered by ajr111
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

\therefore \underline {\boxed{k = 1}}

Hope it helps

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Answered by nithya12333
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

Hope this may help you

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