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!!!

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Question 165601: 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 ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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).
:
Assume you mean, "determine a and b so 1 is a zero"
:
Using synthetic division:
..._________________________
1 | 5 - 3 + a + b - 7
.........+ 5 + 2 +(2+a)+(2+a+b);using this to form an equation with -7
.....--------------------------
......5 + 2+(2+a)+(2+a+b)
:
2 + a + b - 7 = 0; the remainder is 0
a + b - 5 = 0
a + b = 5
:
Try the integers a=2,b=3
..._______________________-
1 | 5 - 3 + 2 + 3 - 7
.........+ 5 + 2 + 4 + 7
......--------------------------
......5 + 2 + 4 + 7 + 0
:
:
5x^4 - 3x^3 + 2x^2 + 3x - 7; is our solution
:
It's interesting that the integers a=1; b=4 will also work and vice versa
:
Hope this made sense to you.