if m and n are zeros of the quadratic polynomial f(x)= x^2-px+q,prove that (m/n)^2+(n/m)^2=p^4/q^2-4p^2/q+2

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α

β

f (x) = x^{2} - p x + q

\frac{α^{2}}{β^{2}} + \frac{β^{2}}{α^{2}}

\frac{p^{4}}{q^{2}} - \frac{4 p^{2}}{q} + 2

α, β

x^{2} - p x + q = 0

α - 2, β + 2

x^{2} - p x + r = 0

16 q + (r + 4 - q)^{2} = 4 p^{2}

If x + a is a common factor of expressions $f (x) = x^{2} + p x + q a n d g (x) = x^{2} + m x + n;$ show that : $a = \frac{n - q}{m - p}$

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