Find the equation whose roots are 2 and \(-3\frac{1}{2}\)
MATHEMATICS
WAEC 2005
Find the equation whose roots are 2 and \(-3\frac{1}{2}\)
- A. 2x2 + 3x + 14 = 0
- B. 2x2 + 5x + 7 = 0
- C. 2x2 + 5x - 7 = 0
- D. 2x2 + 3x - 14 = 0
Correct Answer: D. 2x2 + 3x - 14 = 0
Explanation
x2 (sum of roots)x + (product of roots) = 0
Sum of roots \(2+-3\frac{1}{2} = -1\frac{1}{2}=-\frac{1}{2}\)
Product of roots \(=2 \times -3\frac{1}{2}=-7\\
x^2-\left(\frac{-3}{2}\right)x+(-7)=0\Rightarrow 2x^2 + 3x - 14 = 0\)
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