Quadratic equations

You can always reduce a quadratic equation to this form, which is called general form:

Examples:

1) 3x² - 5x + 2 = 0 a = 3 b = -5 c = 2

2) x² – 3 = 0 a = 1 b = 0 c = -3

3) 2x² – 100x = 0 a = 2 b = -100 c = 0

4) (x + 2) · (x – 3) = 14; x² + 2x – 3x – 6 = 14
                 x^₂ + 2x – 3x – 6 – 14 = 0
                x² – x – 20 = 0; a = 1, b = -1, c = -20
                                                   The solutions to this one are x = 5 and x = -4

To solve a quadratic equation, we have to use the formula:

Example 1:

Example 2:

Example 3:

Example 4:

NOTE: The discriminant, Δ = b² – 4ac, is the value which detemines the number of solutions: if Δ > 0 there are two solutions; if Δ = 0 there is one solution and if Δ < 0 there is no solution.

INCOMPLETE EQUATIONS

Example 5: b = c = 0