Further Maths Past Questions and Answers

The roots of the equation \(2x^{2} + kx + 5 = 0\) are \(\alpha\) and \(\beta\), where k is a constant. If \(\alpha^{2} + \beta^{2} = -1\), find the values of k.

Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).

Find the sum of the exponential series \(96 + 24 + 6 +...\)

Express \(\frac{1}{1 - \sin 45°}\) in surd form.

Evaluate \(\log_{0.25} 8\)