If \(f(x) = 2x^{2} - 3x - 1\), find the value of x for which f(x) is minimum.

The polynomial \(2x^{3} + x^{2} - 3x + p\) has a remainder of 20 when divided by (x - 2). Find the value of constant p.

If \(2\log_{4} 2 = x + 1\), find the value of x.

Which of the following quadratic curves will not intersect with the x- axis?

What is the coordinate of the centre of the circle \(5x^{2} + 5y^{2} - 15x + 25y - 3 = 0\)?