# The Quadratic Formula

A quadratic equation is an equation of the form

where a, b, and c are real numbers and a ≠ 0

The quadratic formula is : If
, then

The quadratic formula is: If , then

a = 1, b = 3, and c = −7

This expression gives two answers .

The quadratic formula is : If , then

a = 2, b = -5, and c = 3

The solutions are rational . We

could have factored .

If , then

a = 3, b = -5, and c = 1

If , then

a = 2, b = -4, and c = -1

If , then

a = 1, b = -2, and c = -10

The quadratic formula is : If , then

The sum of the two solutions will always be

The product of the two solutions will always be

x^{2} – 5x – 14 = 0

x = 7 or x = – 2

7 + (-2) = 5

7 (-2) = -14

The sum of the two solutions will always be

The product of the two solutions will always be

8x^{2} + 14x + 3 = 0.

(4x + 1)(2x + 3) .

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