If $\alpha$ and $\beta$ are the roots of $x^2 - 7x + 10 = 0$, what is $\alpha^2 + \beta^2$?

Explanation

1. 01

   $\alpha + \beta = 7$ and $\alpha\beta = 10$.

2. 02

   $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 49 - 20 = 29$.

3. 03

   Check with the roots 2 and 5: $4 + 25 = 29$.