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23 June, 12:54

Solve the equation x^5-4x^4+4x^3+2x^2-5x+2=0

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  1. 23 June, 13:24
    0
    x = 2 or x = 1 or x = - 1

    Step-by-step explanation:

    Solve for x over the real numbers:

    x^5 - 4 x^4 + 4 x^3 + 2 x^2 - 5 x + 2 = 0

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

    (x - 2) (x - 1) ^3 (x + 1) = 0

    Split into three equations:

    x - 2 = 0 or (x - 1) ^3 = 0 or x + 1 = 0

    Add 2 to both sides:

    x = 2 or (x - 1) ^3 = 0 or x + 1 = 0

    Take cube roots of both sides:

    x = 2 or x - 1 = 0 or x + 1 = 0

    Add 1 to both sides:

    x = 2 or x = 1 or x + 1 = 0

    Subtract 1 from both sides:

    Answer: x = 2 or x = 1 or x = - 1
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