WAEC 2011 Mathematics · Question 10
From the equation whose roots are x = and -
Options
- A.6x2 - x + 2 = 0
- B.6x2 - x - 2 = 0
- C.6x2 + x + 2 = 0
- D.6x2 + x - 2 = 0
Answer: D. 6x2 + x - 2 = 0
Explanation written with AI and checked against the answer key
Analyze the question: We need to form a quadratic equation whose roots are x = 1/2 and x = -2/3. Concept: If the roots are α and β, the equation is x² − (α + β)x + αβ = 0 Solution: Sum of roots: α + β = 1/2 + (−2/3) = 3/6 − 4/6 = −1/6 Product of roots: αβ = (1/2)(−2/3) = −2/6 = −1/3 Substitute into the formula: x² − (−1/6)x + (−1/3) = 0 x² + (1/6)x − 1/3 = 0 Multiply through by 6 to clear the fractions: 6x² + x − 2 = 0 Check using factors: (2x − 1)(3x + 2) = 6x² + 4x − 3x − 2 = 6x² + x − 2 ✓ This matches option D. Tip: Quickly check the signs. The constant term is negative because the roots have opposite signs (product is negative). That eliminates A and C immediately. Then the sum of roots is −1/6, so the x coefficient must be positive when the x² coefficient is 6, which gives D.AI can make mistakes. Report anything that looks wrong.
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