The roots of the quadratic equation \(2x^{2} - 5x + m = 0\) are \(\alpha\) and \(\beta\), where m is a constant. Find \(\alpha^{2} + \beta^{2}\) in terms of m

A.

\(\frac{25}{4} - m\)

B.

\(\frac{25}{4} - 2m\)

C.

\(\frac{25}{4} + m\)

D.

\(\frac{25}{4} + 2m\)

Correct answer is A

\(2x^{2} - 5x + m = 0\)

\(a = 2, b = -5, c = m\)

\(\alpha + \beta = \frac{-b}{a} = \frac{5}{2}\)

\(\alpha \beta = \frac{c}{a} = \frac{m}{2}\)

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

= \((\frac{5}{2})^{2} - 2(\frac{m}{2}) \)

= \(\frac{25}{4} - m\)