THE QUADRATIC FORMULA 

Solve each of the following quadratic equations using the quadratic formula.

Example 1 :

x² – 5x + 6 = 0

Solution :

Comparing ax² + bx + c = 0 and x² – 5x + 6 = 0, we get

a = 1, b = -5, c = 6

Quadratic Formula :

Substitute a = 1, b = -5 and c = 6.

x = 3  or  2

Example 2 :

x² – 2x – 2 = 0

Solution :

Comparing ax² + bx + c = 0 and x² – 2x – 2 = 0, we get

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

Substitute the above values into the quadratic formula.

x = 1 + √3  or  1 - √3

Example 3 :

3x² – 4x – 9 = 0

Solution :

Comparing ax² + bx + c = 0 and x² – 2x – 2 = 0, we get

a = 3, b = -4, c = -9

Substitute the above values into the quadratic formula.

Example 4 :

x² - 9x + 27 = 0

Solution :

Comparing ax² + bx + c = 0 and x² - 9x + 27 = 0, we get

a = 1, b = -9, c = 27

Substitute the above values into the quadratic formula.

Example 5 :

3x² - 2√3x - 5 = 0

Solution :

Comparing ax² + bx + c = 0 and x² - 9x + 27 = 0, we get

a = 3, b = -2√3, c = -5

Substitute the above values into the quadratic formula.

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