## Quadratic Formula

A method for solving quadratic equations involves the quadratic
equation. An equation of the form:

ax

has the following solution(s) for x:

The value of the terms under the radical, which is referred to as the
discriminant, is represented by the Greek letter delta as follows:

Example #1:

ax

^{2}+ bx + c = 0*a*≠ 0has the following solution(s) for x:

Δ
= b^{2} − 4ac

1) For Δ = b^{2} − 4ac >
0:

Equation has two real and unequal roots (Reference Example #1 below)

2) For Δ = b^{2} − 4ac = 0:

Equation has a single root (double root) (Reference Example #2 below)

3) For Δ = b^{2} − 4ac < 0:

Equation has no real roots; its roots are two complex numbers that are complex conjugates of each other (Reference Example #3 below)

Example #1:

Solve the equation x

^{2}+ 7x + 6 = 0Solution #1:

Example #2:

Solution #2:

Example #3:

Solution #3:

Example #2:

Solve the equation x

^{2}− 4x + 4 = 0Solution #2:

Example #3:

Solve the equation 6x

^{2}+ 2x + 1 = 0Solution #3:

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