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7 March, 18:33

Write each quadratic function below in terms of linear factors. a) f (x) = x²-25b) f (x) = x²+25c) f (x) = 4x²+25d) f (x) = x²-2x+1e) f (x) = x²-2x+4

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  1. 7 March, 20:29
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    a) (x + 5) (x - 5)

    b) (x + 5i) (x - 5i)

    c) (x + (5i/2)) (x - (5i/2))

    d) (x-1) (x-1)

    e) x + i√3 + 1) (x - i√3+1)

    Step-by-step explanation:

    To solve this, we will need to factorize each quadratic function making it equal to zero first and then proceeding to find x

    a) f (x) = x²-25

    x²-25 = 0

    ⇒ (x + 5) (x - 5)

    b) f (x) = x²+25

    x² + 25 = 0

    x² = - 25

    x = √-25

    x = √25i

    x = ±5i

    ⇒ (x + 5i) (x - 5i)

    c) f (x) = 4x²+25

    4x²+25 = 0

    4x² = - 25

    x² = - 25/4

    x = ±√ (-25/4)

    x = ± (√25i) / 2

    x = ±5i / 2

    ⇒ (x + (5i/2)) (x - (5i/2))

    d) f (x) = x²-2x+1

    x²-2x+1 = 0

    ⇒ (x - 1) ²

    e) f (x) = x²-2x+4

    x²-2x+4 = 0

    x²-2x = - 4

    x²-2x + 1 = - 4 + 1

    x²-2x + 1 = - 3

    (x-1) ² + 3 = 0

    (x-1) ² = - 3

    x-1 = √-3

    x = ±√3i + 1

    ⇒ (x + i√3 + 1) (x - i√3+1)
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