WAEC 2015 Mathematics · Question 25
Find the equation whose roots are and -4
Options
- A.4x2 - 13x + 12 = 0
- B.4x2 - 13x - 12 = 0
- C.4x2 + 13x - 12 = 0
- D.4x2 + 13x + 12 = 0
Answer: C. 4x2 + 13x - 12 = 0
Explanation written with AI and checked against the answer key
Analyze the question: We need a quadratic equation whose roots (solutions) are 3/4 and -4. Concept: If the roots are α and β, the equation is x² − (α + β)x + αβ = 0 Solution: Sum of roots: α + β = 3/4 + (−4) = 3/4 − 16/4 = −13/4 Product of roots: αβ = (3/4)(−4) = −3 Substitute into the formula: x² − (−13/4)x + (−3) = 0 x² + (13/4)x − 3 = 0 Multiply through by 4 to clear the fraction: 4x² + 13x − 12 = 0 Check using factors: (4x − 3)(x + 4) = 4x² + 16x − 3x − 12 = 4x² + 13x − 12 ✓ If x = 3/4, then 4x − 3 = 0. If x = −4, then x + 4 = 0. Both roots work. Answer: The equation is 4x² + 13x − 12 = 0, which is option C. Tip: Watch the signs. The middle term takes the opposite sign of the sum of the roots, and the last term takes the same sign as the product. Here the sum is negative, so the middle term is positive (+13x). The product is negative, so the constant is negative (−12). This lets you eliminate options A, B, and D quickly.AI can make mistakes. Report anything that looks wrong.
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