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!!!
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(2103) (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
