algebra 2

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write a polynomial function of least degree that has real coefficeints the given zeros and a leading coefficient of 1. the problem is 5,2i,-2i

  • algebra 2 -

    *i think you mean the ZEROS / ROOTS are 5, 2i and -2i.

    if so, you can get them by multiplying and expanding,
    (x-5)(x-2i)(x+2i)
    note that 1 = sqrt(-1)

    but an easier method would be, to start with the roots 2i and -2i. recall that q quadratic equation follows the formula,
    x^2 - (sum of roots)*x + (product of roots)
    thus, substituting 2i and -2i:
    x^2 - (2i - 2i)*x + (2i)*(-2i)
    x^2 - (0)*x - 4*(i^2)
    x^2 - 4*(-1)
    x^2 + 4
    now, we multiply this by (x-5):
    (x-5)(x^2 + 4)
    x^3 - 5x^2 + 4x - 20

    hope this helps~ :)

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