If α and β are the roots of the quadratic equation 2x² - 7x + 4 = 0, find the numerical value of α + β + αβ.
Answer and explanation
Correct answer: A. 5.5
- Step 1: Sum of roots: α + β = -b / a = -(-7) / 2 = 7/2 = 3.5. Step 2. Product of roots: αβ = c / a = 4 / 2 = 2.0. Step 3. Add: (α + β) + αβ = 3.5 + 2.0 = 5.5. Answer: 5.5. Why not the others: 3.5 is the sum of roots alone; 2.0 is the product of roots alone; 7.5 adds an extra 2.0.
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