The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they?

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they?

    A few things to note:
    • X-intercepts are found when y (or f(x)) is 0.
    • On the right side, we have 3 monomials.
    • Therefore, y or f(x) could be 0 when any of these monomials is 0

    The 3 monomials are:
    1. 2x - 3 = 0
    2. x - 4 = 0
    3. x + 3 = 0

    Find all 3 x-intercepts:
    1. 2x - 3 = 0. Using our equation calculator, we see that x = 3/2 or 1.5
    2. x - 4 = 0 Using our equation calculator, we see that x = 4
    3. x + 3 = 0 Using our equation calculator, we see that x = -3
    So our 3 x-intercepts are:
    x = {-3, 3/2, 4}
     

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