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List all possible rational roots, use synthetic division to find an actual root, then use this root to solve the equation.
x^3 -7x^2 +13x -7=0

  • Math -

    possible rational roots are ±1,±7
    division show 1 is a root
    x^3 -7x^2 +13x -7 = (x-1)(x^2 - 6x + 7)
    so the roots are 1 and 3±√2

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