WAEC 2023 Mathematics · Question 48
The truth set of = 0 is {p, q}. Evaluate p + q.
Options
- A.4
- B.2
- C.-6
- D.-2
Answer: B. 2
Explanation written with AI and checked against the answer key
Analyze the question: We need the roots p and q of 8 + 2x − x² = 0, then find their sum. Concept: For a quadratic ax² + bx + c = 0, the sum of the roots is −b/a. We can also confirm by factorising. Solution: Rearrange into standard form by multiplying through by −1: x² − 2x − 8 = 0 Factorise: we need two numbers that multiply to −8 and add to −2. Those are −4 and +2. (x − 4)(x + 2) = 0 So x = 4 or x = −2, which means p = 4 and q = −2. p + q = 4 + (−2) = 2 Check using the formula: In x² − 2x − 8 = 0, a = 1 and b = −2, so the sum of the roots is −b/a = −(−2)/1 = 2. ✓ Answer: The sum is 2, which is option B. Tip: You don't even need to find the roots. For ax² + bx + c = 0, the sum is −b/a and the product is c/a. Just be careful with signs when the x² term is negative. In the original form, a = −1 and b = 2, so −b/a = −2/(−1) = 2, which gives the same result.AI can make mistakes. Report anything that looks wrong.
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