If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 7x + 4

Explanation

\(2x^{2} - 7x + 4 = 0\)

\(\alpha + \beta = \frac{7}{2}\)

\(\alpha \beta = \frac{4}{2} = 2\)

\(\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^{2} + \beta^{2}}{\alpha \beta}\)

= \(\frac{(\alpha + \beta)^{2} - 2\alpha \beta}{\alpha \beta}\)

= \(\frac{(\frac{7}{2})^{2} - 2(2)}{2}\)

= \(\frac{(\frac{49}{4} - \frac{16}{4})}{2}\)

= \(\frac{33}{8}\)

\(\frac{\alpha}{\beta} \times \frac{\beta}{\alpha} = 1\)

\(\therefore Equation : x^{2} - \frac{33}{8}x + 1 = 0\)