Finding the coefficients in a quadratic equation when you know the two roots

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.