NECO 2008 Mathematics · Question 1
Construct a quadratic equation whose roots are - and 7
Options
- A.3x2 + 11x + 21 = 0
- B.2x2 + 11x + 21 = 0
- C.2x2 - 11x – 21 = 0
- D.3x2 - 11x - 21 = 0
- E.x2 - 11x – 21 = 0
Answer: C. 2x2 - 11x – 21 = 0
Explanation written with AI and checked against the answer key
Step 1: Analyze the question We need a quadratic equation whose roots are -3/2 and 7. Step 2: The concept If the roots are α and β, the equation is: x² − (α + β)x + αβ = 0 Step 3: Solution Sum of roots: α + β = -3/2 + 7 = -3/2 + 14/2 = 11/2 Product of roots: αβ = (-3/2)(7) = -21/2 Substitute into the formula: x² − (11/2)x + (−21/2) = 0 x² − (11/2)x − 21/2 = 0 Multiply every term by 2 to clear the fractions: 2x² − 11x − 21 = 0 Check using factors: x = -3/2 → 2x = -3 → (2x + 3) = 0 x = 7 → (x − 7) = 0 (2x + 3)(x − 7) = 2x² − 14x + 3x − 21 = 2x² − 11x − 21 ✓ Step 4: Answer The equation is 2x² − 11x − 21 = 0, which is option C. Tip: When a root is a fraction like -3/2, turn it into a factor with the fraction's denominator on x: x = -3/2 becomes (2x + 3). Also, quickly eliminate options using the sign pattern: the sum is positive (11/2), so the x-term must be negative, and the product is negative, so the constant must be negative. Only C, D and E have that pattern, and only C has the right coefficients.AI can make mistakes. Report anything that looks wrong.
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