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find a possible polynomial equation of degree 4 if the zeroes are -1,2, and 5, the graph touches the x-axis at -1 but does not cross through, and the y intercept is -5

  • Pre-calc - ,

    there must be double root at x = -1
    so it must be
    y = a(x-2)(x-5)(x+1)^2
    also we know (0,-5) lies on it, so

    -5 = (-2)(-5)(1)
    -5 = 10a
    a = -1/2

    with your information there is a unique polynomial of
    y = (-1/2)(x-2)(x-5)(x+1)^2

    expand if need be.

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