Mathematics Past Questions and Answers

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).

The function f: x \(\to \sqrt{4 - 2x}\) is defined on the set of real numbers R. Find the domain of f.

Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).

Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}\), find the value of m.

Find the coefficient of \(x^{4}\) in the expansion of \((1-2x)^{6}\).