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what is the root of 4x to the 4th power + 8x to the 3rd power - 13x to the 2nd power -2x +3

3 answers

  1. I think you mean
    (√(4x))^4 + 8x^3 - 13x^2 - 2x + 3
    which is
    16x^2 + 8x^3 - 13x^2 - 2x + 3
    = 8x^3 + 3x^2 - 2x + 3

    Now what about it?
    What do want done with it?

  2. I need the roots of 4x^4+8x^3-13x^2-2x+3

  3. Read your first line, can you see how it can be misinterpreted?

    so let
    f(x) = 4x^4+8x^3-13x^2-2x+3

    try x = ±1, ±3
    f(1) = 0, so x-1 is a factor,
    I then used synthetic division to show that
    4x^4+8x^3-13x^2-2x+3 = (x-1)(4x^3 + 12x^2 - x - 3)

    but (4x^3 + 12x^2 - x - 3)
    = 4x^2(x+3) - (x+3)
    = (x+3)(4x^1 - 1)
    = (x+3)*2x-1)(2x+1)

    so for
    4x^4+8x^3-13x^2-2x+3 = 0
    (x-1)x+3)(2x+1)(2x-1) = 0
    x = 1, -3, ±1/2

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