The problem is...

Find a, b, c if...

$\displaystyle P(x)=ax^2+bx+c$ AND $\displaystyle P(3+4i)=0$ and $\displaystyle P(3-4i)=0$

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 $\displaystyle -b\pm\sqrt{b^2-2c}$

I figured b must equal -3 so that -b=3.

I also figured that c must equal 12.5 so that the radical becomes $\displaystyle \sqrt{-16}$

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.