Question

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

Answer 1

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)