SOLUTION: PLEASE, PLEASE HELP ME!!! Given {{{ 5x^4 - 3x^3 + ax^2 + bx - 7 = 0 }}} determine a and b so that i is a zero of the quartic. THANK YOU FOR ANY HELP YOU CAN GIVE!!!!

Algebra ->  Functions -> SOLUTION: PLEASE, PLEASE HELP ME!!! Given {{{ 5x^4 - 3x^3 + ax^2 + bx - 7 = 0 }}} determine a and b so that i is a zero of the quartic. THANK YOU FOR ANY HELP YOU CAN GIVE!!!!      Log On


   

Question 239705: PLEASE, PLEASE HELP ME!!!
Given +5x%5E4+-+3x%5E3+%2B+ax%5E2+%2B+bx+-+7+=+0+ determine a and b so that i is a zero of the quartic.

THANK YOU FOR ANY HELP YOU CAN GIVE!!!!
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
5x^4 - 3x^3 + ax^2 + bx - 7 = 0
f(i)=5-3(-i)-a+bi-7=0
-3(-i)-a+bi=2 because 5-7=-2
-3(-i)+bi=2+a
.
f(-i)=5-3i-a+b(-i)-7=0 If one zero is i then another must be -i.
-3i-a+b(-i)=2
-3i+b(-i)=2+a
.
-3(-i)+bi=-3i+b(-i) Since they both equal 2+a.
-3-b=3+b multiply each side by i.
2b=-6
b=-3
.
a=-3(-i)-3i-2
a=-2
.
It checks.
This WAS tough!
.
Ed