SOLUTION: for what value(s) of p does the equation x^2+px+1=0 have no real solutions, and two real solutions.

Question 155038: for what value(s) of p does the equation x^2+px+1=0 have no real solutions, and two real solutions.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
For this discussion, we'll use the discriminant.
For the general quadratic equation,

the discriminant is

.
.
If then you have two distinct real roots.
If , you have a double root, one real root occurring twice
If , you have two complex roots, that are complex conjugates.

For no real (complex) solutions,

Valid interval: ()
.
.
.
.
For two real solutions,

and
Valid interval:(,]U[,)
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