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if f(x) and g(x) are 2 polynomials such that h(x)=xf(x 3 )+xg(x 6 ) is divisible by x 2 +x+1 then 1)f(1)=g(1) 2)f(1)=g(1)=0(not equal to zero) 3)f(1)=-g(1) 4)f(1)=-g(1)=0(not equal to zero)

if f(x) and g(x) are 2 polynomials such that 
h(x)=xf(x3)+xg(x6) is divisible by x2+x+1 then
1)f(1)=g(1)
2)f(1)=g(1)=0(not equal to zero)
3)f(1)=-g(1)
4)f(1)=-g(1)=0(not equal to zero)

Grade:12

1 Answers

Vikas TU
14149 Points
7 years ago
Roots of x2+x+1 are imaginary that are w and w^2 which are the cubic roots.
Hence this would satify the h(w) eqn.
Therfore,
h(w) = 0 => wf(1) + wg(1) = 0
or
w(f(1) + g(1)) = 0
w cannot be zero hence obvious
f(1) + g(1) = 0.
Third option

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