The quadratic equation $x^{2}-px+q=0$ has two distinct positive roots $r$ and $s$ such that $r+s=7$ and $\frac{1}{r}+\frac{1}{s}=\frac{2}{5}$. Find the values of $p$ and $q$ and then compute $r^{2}+s^{2}$.

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p = 7, q = \frac{35}{2}, r^{2}+s^{2}=14

Neco 2024 Mathematics Question 41

The quadratic equation \(x^{2}-px+q=0\) has two distinct positive roots \(r\) and \(s\) such that \(r+s=7\) and \(\frac{1}{r}+\frac{1}{s}=\\frac{2}{5}\). Find the values of \(p\) and \(q\) and then compute \(r^{2}+s^{2}\).

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