quadratic eqns w/ complex solns: given one soln, find other

[sisterofmaddie]

Given that "2 - i" is a solution of a quadratic equation with real coefficients, find the other solution.

I really am not sure how to attack this problem. It seems like you need to work backwards, but I just don't know what to do. Please help!

 

[arthur ohlsten]

x=[2-i] is one root
for the equation to have no imaginary terms the second root must be
x=2+i
y=[x+i][x-i]
y=x^2-1

y=ax^2+bx+c
y=-b+/-[b^2-4ac]^1/2 all over 2a

to have a complex root
4ac>b^2; assume this is true,then the two roots are
x=[-b+ni]/2a AND x=[-b-ni]/2a
"conjugate" terms
Arthur