Question

- If (x^100+2x^99+k) is divisible by (x+1), then the value of k​

Answer 1

Answer:

k=1

Step-by-step explanation:

f(x)=x^100+2x^99+k

If f(x) is divisible by x+1

then x+1 is factor of f(x)

so x+1=0

or x=-1

hence f(-1)=0

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(-1¹⁰⁰+2(-1)⁹⁹+k=0

=[ (-1)² ]⁵⁰+ 2*(-1)¹(-1)⁹⁸+k=0

=(1)⁵⁰+ 2*(-1) [ (-1)² ]⁴⁹+k=0

=1 - 2*1(1)⁴⁹+k=0

1-2*1*1+k = 0

1-2+k=0

k=1