SOLUTION: 1. How many solutions exist for a quadratic equation? Explain and example 2. How do we determine whether the solutions are real or complex? Example.

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1.There are always two solutions to a quadratic equation.
They may be a complex conjugate pair solution or a real solution, which includes the possibility of a double root at one x value.
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2. Graphically, you can graph the function and see if it ever crosses the x axis. If it does, then the roots are real, if not, then the roots are complex.
Algebraically, use the discriminant,
where the quadratic equation is in the form .
If , two real distinct roots.
If , one real double root.
If , two complex conjugate pair roots.
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The red curve has two real roots, ,
The green curve has one real double root, ,
The blue curve has complex conjugate roots, ,