If x100-2 x99-k is divisible by x-1- then the value of k isA- 3B- -2C- 1D- -3

The correct option is C 1 Since (x+1) is a factor, x = 1 nbsp;will make the given expression zero. ∴ ( 1)^100 nbsp;+ nbsp;2 × ( 1)^99 + k nbsp;= 0 ...

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Byju's Answer

Standard VIII

Mathematics

Powers with Negative Exponents

If x100+2 x99...

Question

If $x^{100} + 2 x^{99} + k$ is divisible by $(x + 1)$ , then the value of $k$ is

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Solution

The correct option is A
1

Since $(x + 1)$ is a factor, $x = - 1$ will make the given expression zero.

$∴ (- 1)^{100} + 2 \times (- 1)^{99} + k = 0 \Rightarrow 1 - 2 + k = 0 \Rightarrow k = 1$

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

The correct option is A 1 Since (x+1) is a factor, x=−1 will make the given expression zero. ∴(−1)100+2×(−1)99+k=0⇒1−2+k=0⇒k=1

If $x^{100} + 2 x^{99} + k$ is divisible by $(x + 1)$ , then the value of $k$ is

The correct option is A
1

Since $(x + 1)$ is a factor, $x = - 1$ will make the given expression zero.

$∴ (- 1)^{100} + 2 \times (- 1)^{99} + k = 0 \Rightarrow 1 - 2 + k = 0 \Rightarrow k = 1$