Two numbers with given sum and product

Text

Find two numbers whose sum is $9$ and whose product is $20$.

Solution

The two numbers are roots of $t^{2}-St+P=0$ with $S=9$, $P=20$: $t^{2}-9t+20=0\;\Rightarrow\;(t-4)(t-5)=0.$ So the numbers are $4$ and $5$. $\boxed{\,4\ \text{and}\ 5\,}$