If α and β are the roots of the quadratic equation x² - 4x + 2 = 0, find the numerical value of α² + β².
Answer and explanation
Correct answer: C. 12
- Step 1: Sum of roots: α + β = 4; Product of roots: αβ = 2. Step 2. Identity for sum of squares: α² + β² = (α + β)² - 2αβ. Step 3. Substitute values: α² + β² = 4² - 2(2) = 16 - 4 = 12. Answer: 12. Why not the others: 16 is (α + β)² without subtracting 2αβ; 8 subtracts 4(2); 14 subtracts only αβ.
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