n = 4; i and 2 i are zeros; f(-1)=30

Answered question

2022-02-16

n = 4; i and 2 i are zeros; f(-1)=30

Answer & Explanation

Vasquez

Vasquez

Expert2022-03-13Added 669 answers

i and 2i be the zeros

2i be also a zero

f(x) is of 4th degree

f(x)=(xi)(x+i)(x2i)(x+2i)=(xx+xiixii)(x2i)(x+2i)=(x2+1)(x2i)(x+2i)=(x2x+x2(2i)+1x+1(2i))(x+2i)=(x3+x2(2i)+x2i)(x+2i)=x3x+x3(2i)+x2(2i)x+x2(2i)(2i)+x+x(2i)2ix2i(2i)=x4+5x2+4

Also,
f(1)=(1)4+5(1)2+4=1+5+4=10

That is false.

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