The equation x² - 13x + c = 0 has two real solutions that differ by 3. What is the value of c?

Let the roots be $r$ and $r + 3$. The sum of the roots of $x^2 - 13x + c = 0$ is 13, so $2r + 3 = 13$ and $r = 5$. The roots are 5 and 8, and $c$ is their product: $5 \times 8 = 40$. Check: $x^2 - 13x + 40 = (x - 5)(x - 8)$, and $8 - 5 = 3$. A common wrong answer is 42, from using the roots 6 and 7, which sum to 13 but differ by only 1. Another is 13, the sum of the roots, which is the $x$-coefficient and not $c$. A third is 10, which comes from halving 13 incorrectly.