Given that \(\alpha\) and \(\beta\) are the roots of an equation such that \(\alpha + \beta = 3\) and \(\alpha \beta = 2\), find the equation.

Which of the following is the same as \(\sin (270 + x)°\)?

The sum of the first three terms of an Arithmetic Progression (A.P) is 18. If the first term is 4, find their product.

Given that the straight lines \(kx - 5y + 6 = 0\) and \(mx + ny - 1 = 0\) are parallel, find a relationship connecting the constants m, n and k.

Two functions f and g are defined on the set R of real numbers by \(f : x \to 2x - 1\) and \(g : x \to x^{2} + 1\). Find the value of \(f^{-1} \circ g(3)\).

The binary operation * is defined on the set of R, of real numbers by \(x * y = 3x + 3y - xy, \forall x, y \in R\). Determine, in terms of x, the identity el...

The gradient of the line passing through the points P(4, 5) and Q(x, 9) is \(\frac{1}{2}\). Find the value of x.

Simplify \(\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°}\)

Simplify \(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} +1}\)