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5 October, 14:45

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

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Answers (1)
  1. 5 October, 15:36
    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)
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