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Math Help - Few Questiosn regarding Graphs and equations

  1. #1
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    Few Questiosn regarding Graphs and equations

    1.Find a cubic equation with integral coefficients with roots 3i and -5

    2.Does this work with quadratic equations as well?

    3.Find all real and imaginary roots of X^3-3x^2+4x-12=0(do i use synthetic division to find all the roots?)
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  2. #2
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    Quote Originally Posted by xian791 View Post
    1.Find a cubic equation with integral coefficients with roots 3i and -5

    2.Does this work with quadratic equations as well?

    3.Find all real and imaginary roots of X^3-3x^2+4x-12=0(do i use synthetic division to find all the roots?)
    1. y = k(x + 3i)(x - 3i)(x + 5)

    2. yes

    3. x^3-3x^2+4x-12=0

    x^2(x - 3) + 4(x - 3) = 0

    (x-3)(x^2+4) = 0

    finish up
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  3. #3
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    for the first one, how did you get the answer? What does k stand for and you add and subtract 3i, but why not add and subtract 5?
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  4. #4
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    k is just a constant which depends on what points (x,y) the cubic function passes through.

    if a polynomial has a root a + bi, then its conjugate a - bi is also a root.

    5 is a single root.
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  5. #5
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    im still a bit confused on the answer...

    lets say they gave u 8 and 3 and they wanted you to find the quadratic equation.How would you solve it?
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  6. #6
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    if x = 8 and x = 3 are zeros of the quadratic function, then y = k(x-3)(x-8)
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