#### Question

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.

Question

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\times 16= 148

Therefore, the quadratic equation is x^2-24x+148=0