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Produce a third degree polynomial that has exactly the roots -3 and 5 with y-intercept 1350.

I understand I could start with (x+3)(x-5)^2, but i don't know how to get the y-intercept 1350 with the same conditions. Please help. thank you.

  • Algebra -

    you are only given two roots, so let the equation be

    y = (x+3)(x-5)(x-a)
    but you know that (0,1350) lies on it
    1350 = (3)(-5)(-a)
    1350 = 15a
    a = 90

    so equation is
    y = (x+3)(x-5)(x-90)

    expand if you have to, it is more useful in factored form.

    btw, your equation of y = ....(x-5)^2 would have a double root of 5, that is, it would "touch" the x-axis at x = 5

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