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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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\(^2\) - \(\frac{-3}{2}\)x + (-7) = 0 ⇒ 2x\(^2\) + 3x - 14 = 0
Source: Myschool Past Questions Archive (Record #26674)