The sum and product of the roots of a quadratic equation are \(\frac{4}{7}\) and \(\frac{5}{7}\) respectively. Find its equation.

\(f(x) = (x^{2} + 3)^{2}\) is defines on the set of real numbers, R. Find the gradient of f(x) at x = \(\frac{1}{2}\).

Find \(\lim \limits_{x \to 3} \frac{x + 3}{x^{2} - x - 12}\)

If \(y^{2} + xy - x = 0\), find \(\frac{\mathrm d y}{\mathrm d x}\).

A line is perpendicular to \(3x - y + 11 = 0\) and passes through the point (1, -5). Find its equation.