If and are roots of , then
and .
Simplifying equation 1:
Therefore and when you equate real and imaginary parts.
Now do the same with Equation 2, and solve the resulting system for .
The problem is...
Find a, b, c if...
AND and
So, we know that 3+4i and 3-4i are two roots (imaginary).
The way I approached this problem is I looked at the quadratic formula and I set a to a value such that the denominator equals 1.
So, I let a=.5
The formula becomes
I figured b must equal -3 so that -b=3.
I also figured that c must equal 12.5 so that the radical becomes
So i got...
a=.5
b=-3
c=12.5
The answer in the back of the book gives an answer of...
a=1
b=-6
c=25
Basically, they doubled all the coefficients. Are both answers acceptable? If only the books answer is acceptable, how could I solve this problem and arrive at the answer the book provided?
Thanks.