Question

If a and b are the roots of x^2 - 9x + 20 = 0, find a^2 + b^2.

Solution

1. For x^2 - 9x + 20 = 0, the sum of the roots is a + b = 9 and the product is ab = 20.
2. Use the identity a^2 + b^2 = (a + b)^2 - 2ab.
3. a^2 + b^2 = 81 - 40 = 41.
4. Check: the roots are 4 and 5, and 16 + 25 = 41.