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Math Help - Algebraic problem q.

  1. #1
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    Algebraic problem q.

    The roots of x^2 + px + q =0 are doublet he roots of x^2 - (b+c)x + bc =0. Write p and q in terms of b and c.
    Can someone show me how to do this please?
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  2. #2
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    For  x^2 - (b+c)x + bc =0

    Sum of roots is: -\left(\frac{-(b+c)}{1}\right) = b+c

    Product of roots is:  \frac{bc}{1} = bc

    Clearly b and c are the roots of this equation (substitute into the equation and see). Therefore the roots of  x^2 + px + q =0 are 2b and 2c.

    Sum of roots for this equation is  -\frac{p}{1} = -p therefore
     -p = 2b + 2c \Rightarrow p = -2(b+c)

    Product of roots is:  \frac{q}{1} = q therefore

     q = 2b \times 2c = 4bc
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