If ax2 + bx + c = 0 then

1. Solve these quadratic equations using the quadratic formula.

Where necessary, give your answers to 3 significant figures.

(a) 3x2 + 10x + 6 = 0 (b) 5x2 - 6x + 1 = 0

(c) 2x2 - 7x - 15 = 0 (d) x2 + 4x + 1 = 0

3x² + 10x + 6 = 0

x = - (10) ± √ ((10) ² - 4 (3) (6))

2 (3)

x = - 10 ± √ (100 - 72)

6

x = - 10 ± √ (28)

6

x = - 10 ± 2√ (7)

6

x = - 5 ± √ (7)

3

x = - 1²/₃ ± ¹/₃√ (7)

5x² - 6x + 1 = 0

x = - (-6) ± √ ((-6) ² - 4 (5) (1))

2 (5)

x = 6 ± √ (36 - 20)

10

x = 6 ± √ (16)

10

x = 6 ± 4

10

x = 3 ± 2

5

x = 3 + 2 or x = 3 - 2

5 5

x = 5 or x = - 1

5 5

x = 1 or x = - 0.2

2x² - 7x - 15 = 0

x = - (-7) ± √ ((-7) ² - 4 (2) (-15))

2 (2)

x = 7 ± √ (49 + 120)

4

x = 7 ± √ (169)

4

x = 7 ± 13

4

x = 7 + 13 or x = 7 - 13

4 4

x = 20 or x = 6

4 4

x = 5 or x = 1.5

x² + 4x + 1 = 0

x = - (4) ± √ ((4) ² - 4 (1) (1))

2 (1)

x = - 4 ± √ (16 - 4)

2

x = - 4 ± √ (12)

2

x = - 4 ± 2√ (3)

2

x = - 2 ± √ (3)

2

x = - 1 ± ¹/₂√ (3)

x = - 1 + ¹/₂√ (3) or x = - 1 - ¹/₂√ (3)