- #1
utkarshakash
Gold Member
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Homework Statement
Let f(x) = [itex]x^{4}+ax^{3}+bx^{2}+cx+d[/itex] be a polynomial with real coefficients and real zeroes. If |f(i)| = 1, (where [itex]i = \sqrt{-1}[/itex]) then find a+b+c+d.
Homework Equations
The Attempt at a Solution
f(i) = 1-b+d+ci-ai
Taking modulus
|f(i)|= |1-b+d+i(c-a)|
[itex]=(1-b+d)^{2}+(c-a)^{2}=1[/itex]
Simplifying
[itex]a^{2}+b^{2}+c^{2}+d^{2}=2(b-d+bd+ac)[/itex]
But this takes me nowhere close to the answer. What else can I try?