Finding the coefficients in a quadratic equation when you know the two roots
The problem is...
Find a, b, c if...
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...
The answer in the back of the book gives an answer of...
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?