Given that \(\alpha\) and \(\beta\) are the roots of an equation such that \(\alpha + \beta = 3\) and \(\alpha \beta = 2\), find the equation.
A. \(x^{2} - 3x + 2 = 0\)
B. \(x^{2} - 2x + 3 = 0\)
C. \(x^{2} - 3x - 2 = 0\)
D. \(x^{2} - 2x - 3 = 0\)
Correct Answer: A
Explanation
Given \(ax^{2} + bx + c = 0 (\text{general form of a quadratic equation})\)
We have \(x^{2} + \frac{b}{a}x + \frac{c}{a} = 0\)
\( x^{2} - (-\frac{b}{a})x + \frac{c}{a} = 0\)
\(\implies x^{2} - (\alpha + \beta)x + (\alpha \beta) = 0\)
\(\therefore \text{The equation is} x^{2} - 3x + 2 = 0\)
