Construct a quadratic equation whose roots are \(-\frac{1}{2}\) and 2.
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Correct Answer: Option E
Explanation:
If x = \(-\frac{1}{2}\) and 2; then
\(x + \frac{1}{2} = 0\) and \(x - 2 = 0\)
\(\implies (x + \frac{1}{2})(x - 2) = 0\)
\(x^2 - 2x + \frac{1}{2}x - 1 = 0\)
\(x^2 - \frac{3}{2}x - 1 = 0\)
\(2x^2 - 3x - 2 = 0\)
If x = \(-\frac{1}{2}\) and 2; then
\(x + \frac{1}{2} = 0\) and \(x - 2 = 0\)
\(\implies (x + \frac{1}{2})(x - 2) = 0\)
\(x^2 - 2x + \frac{1}{2}x - 1 = 0\)
\(x^2 - \frac{3}{2}x - 1 = 0\)
\(2x^2 - 3x - 2 = 0\)