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Math Help - Find quadratic using its roots.

  1. #1
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    Find quadratic using its roots.

    I was wondering how to go about doing this question:
    Find all quadratics with the roots -3+-2i in the form ax^2 +bx+c=0

    any help is appreciated.
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  2. #2
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    Quote Originally Posted by carmo100 View Post
    I was wondering how to go about doing this question:
    Find all quadratics with the roots -3+-2i in the form ax^2 +bx+c=0

    any help is appreciated.

    This is a nice, little theorem (a particular case of Viete's formulae):

    Theorem: if x_1\,,\,x_2 are the roots of a quadratic equation ax^2+bx+c=0, then x_1x_2=\frac{c}{a}\,,\,\,x_1+x_2=-\frac{b}{a}

    Tonio
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  3. #3
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    Thankyou, this is exactly what I needed.
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  4. #4
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    Also, any quadratic having roots r_1 and r_2 is of the form a(x- r_1)(x+ r_1)= 0. Replace r_1 with -3+ 2i, r_2 with -3- 2i, and multiply that out.

    The easiest way to do that is to think of it as a product of "sum and difference": ((x-3)- 2i)((x-3)+ 2i)
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