If $$m$$ and $$n$$ are the zeroes of the quadratic polynomial such that $$m+n =24$$ and $$m-n=8$$，find a quadratic polynomial having $$m$$ and $$n$$ as its zeroes.

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Uniteasy Admin · Accepted Answer

Let $$x^2+px+q=0$$ be the quadratic that has $$m$$ and $$n$$ as its zeros.
According to Vieta's formula
$$m+n = -p = 24$$ and $$mn=q$$
then p = -24. 
Since $$m-n = 8$$ and $$m+n=24$$
$$q=mn = \dfrac{1}{4} [(m+n)^2-(m-n)^2]$$
$$=\dfrac{1}{4}(24^2-8^2) $$
$$=\dfrac{1}{4}(24+8)(24-8) $$
$$=8	imes 16= 148$$ 
Therefore, the quadratic equation is $$x^2-24x+148=0$$

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