WAEC 2016 Mathematics · Question 47
The roots of a quadratic equation are and -. Find the equation
Options
- A.21x2 - 19x - 12 = 0
- B.21x2 + 37x - 12 = 0
- C.21x2 - x + 12 = 0
- D.21x2 + 7x - 4 = 0
Answer: A. 21x2 - 19x - 12 = 0
Explanation written with AI and checked against the answer key
Analyze the question: We are given two roots and must build the quadratic equation. Concept: If the roots are α and β, the equation is x² − (α + β)x + αβ = 0 Solution: Sum of roots: 4/3 + (−3/7) = 28/21 − 9/21 = 19/21 Product of roots: (4/3) × (−3/7) = −12/21 Equation: x² − (19/21)x − 12/21 = 0 Multiply through by 21: 21x² − 19x − 12 = 0 Check with the factor method: (3x − 4)(7x + 3) = 21x² + 9x − 28x − 12 = 21x² − 19x − 12. ✔ Answer: A Tip: For roots α and β, remember "x² minus sum times x plus product". Watch the signs: a negative root makes the product negative, which is why the constant term here is −12. Also, after finding the equation, quickly expand the factors to confirm your answer.AI can make mistakes. Report anything that looks wrong.
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