Solving Equations then tell which solution method you used!

G

Guest

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

Full Member
Joined
Dec 14, 2005
Messages
832
The quadratic formula works. The solution will be two conjugate complex numbers.
 
G

Guest

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

Full Member
Joined
Dec 14, 2005
Messages
832
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 \(\displaystyle (x-8-i)(x-8+i)=(x-8)^2-i^2 = x^2-16x+64+1\).
 
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