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# Finding solutions through quadratic equations

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Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as:
1. Integers
2. Rational numbers
3. Irrational numbers

Please see the attached file for the fully formatted problem(s).

1. How many solutions exist for a quadratic equation? How do we determine whether the solutions are real or complex?

2. Look at the graph above and comment on the sign of D or the discriminant. Form the quadratic equation based on the information provided and find its solution.

#### Solution Preview

(a) With Integer coefficients:

3x^2 - 4x + 7 = 0

(b) With Rational Number coefficients

x^2 + (1/2)x + (3/4) = 0

(c) With Irrational Number coefficients

(sqrt 3)x^2 - (sqrt ...

#### Solution Summary

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