college Algebra

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Let g(x) = -2x2 + bx + c be a quadratic function, defined everywhere, where b and c are constants. If x = 1 marks the location of one of the zeros of this quadratic function, and if the y-intercept of this function is at (0, 5), then use this information to name constant b.

  • college Algebra -

    g = -2x^2 + bx + c
    g = (x-1)(-2x + b-2) remainder b+c-2

    In order for 1 to be a root, then x-1 must divide g exactly. That is,

    b+c-2 = 0

    Using the y-intercept, when x=0, y=5
    5 = c

    So, b+3 = 0, or b=-3

    g = -2x^2 -3x + 5 = (x-1)(-2x - 5)

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