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15 May, 06:00

13. f (x) = x^4

- 9x2 - 22x - 24

+4
Answers (1)
  1. 15 May, 09:40
    0
    x = 4 or x = - 2

    Step-by-step explanation:

    Solve for x over the real numbers:

    x^4 - 9 x^2 - 22 x - 24 = 0

    The left hand side factors into a product with three terms:

    (x - 4) (x + 2) (x^2 + 2 x + 3) = 0

    Split into three equations:

    x - 4 = 0 or x + 2 = 0 or x^2 + 2 x + 3 = 0

    Add 4 to both sides:

    x = 4 or x + 2 = 0 or x^2 + 2 x + 3 = 0

    Subtract 2 from both sides:

    x = 4 or x = - 2 or x^2 + 2 x + 3 = 0

    Subtract 3 from both sides:

    x = 4 or x = - 2 or x^2 + 2 x = - 3

    Add 1 to both sides:

    x = 4 or x = - 2 or x^2 + 2 x + 1 = - 2

    Write the left hand side as a square:

    x = 4 or x = - 2 or (x + 1) ^2 = - 2

    (x + 1) ^2 = - 2 has no solution since for all x on the real line, (x + 1) ^2 >=0 and - 2<0:

    Answer: x = 4 or x = - 2
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