Construct a quadratic equation whose roots are \(-\frac{1}{2}\) and 2.
A
3x2-3x+2=0
B
3x2+3x-2=0
C
2x2+3x-2=0
D
2x2-3x+2=0
E
2x2-3x-2=0
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
If x = \(-\frac{1}{2}\) and 2; then
\(x + \frac{1}{2} = 0\) and \(x - 2 = 0\)
\(\implies (x + \frac{1}{2})(x - 2) = 0\)
\(x^2 - 2x + \frac{1}{2}x - 1 = 0\)
\(x^2 - \frac{3}{2}x - 1 = 0\)
\(2x^2 - 3x - 2 = 0\)
Source: Myschool Past Questions Archive (Record #23148)