Solving Equations then tell which solution method you used!

[Guest]

T^2 -16T +65=0

I've tried the Quadratic formula
Factoring and Graphin but 65 only factors are
1 *65 and
5*13???
Any one have any ideas??? Please??? Mom's lost...and My son had left this problem after working on it for over an hour! Thanks Mom :?

 

[royhaas]

The quadratic formula works. The solution will be two conjugate complex numbers.

 

[Guest]

Lost

when I use the formula I come up with a negative 4 in the aquare root which can't be so I get only 16 +/- 0 divided by 2 which gives me only 8 as an answer????

 

[royhaas]

The square root of a negative number is a complex number, sometimes called an imaginary number. You write it as $\displaystyle \sqrt{-4}=2i$, where $\displaystyle i^2 = -1$. So one root will have $\displaystyle +2i$ and the other will have $\displaystyle \ -2i$ as part of the solution. In other words,
$\displaystyle x = 8+i, x=8-i$ is the solution.

The check is that $\displaystyle (x-8-i)(x-8+i)=(x-8)^2-i^2 = x^2-16x+64+1$.