# SOLUTION: Given 5x^4-3x^3+ax^2+bx-7 determine a and b so i is a zero of the quartic (Hint:Use synthetic or long division). Please help me, I just can't find the answer!!!

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Given 5x^4-3x^3+ax^2+bx-7 determine a and b so i is a zero of the quartic (Hint:Use synthetic or long division). Please help me, I just can't find the answer!!!      Log On

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 Click here to see ALL problems on Complex Numbers Question 165600: Given 5x^4-3x^3+ax^2+bx-7 determine a and b so i is a zero of the quartic (Hint:Use synthetic or long division). Please help me, I just can't find the answer!!!Answer by oscargut(891)   (Show Source): You can put this solution on YOUR website!P(x)=5x^4-3x^3+ax^2+bx-7 i is a zero of P(x) then -i is a zero of P(x) too Using synthetic division: Please see source code 5 -3 a b -7 i 5i -5-3i -5i+3+ai 5+3i-a+bi 5 5i-3 -5-3i+a -5i+3+ai+b -2-a+(3+b)i=0 -i -5i 3i 5i-ai 5 -3 -5+a 3+b=0 -2-a+(3+b)i=0 3+b=0 then b=-3 and a=-2 P(x)=5x^4-3x^3-2x^2-3x-7