If α and β are the roots of x² − 5x + 3 = 0, form the equation whose roots are α² and β².

1. 1 · Write what is given and what is to be found. α and β are the roots of x² − 5x + 3 = 0. To find: the equation whose roots are α² and β².
2. 2 · Write the formulas. α + β = −b/a and αβ = c/a. Required equation: x² − (sum of roots)x + (product of roots) = 0.
3. 3 · Find the sum and product of α and β. α + β = 5 and αβ = 3.
4. 4 · Find the new sum. α² + β² = (α + β)² − 2αβ = 25 − 6 = 19.
5. 5 · Find the new product. α²β² = (αβ)² = 9.
6. 6 · Check and box the answer. Substitute in the formula: x² − 19x + 9 = 0. Box it.

Scoring tip: Do not solve for α and β one by one. Use the sum and the product: it is faster, and it is the method examiners expect.