An alternative method to solve a quadratic equation is to complete the square. To solve an equation of the form \(x^2 + bx + c = 0\) consider the expression \(\left(x + \frac{b}{2}\right)^2 + c\).

It is not possible to find the square root of a negative ... or touch the \(x\)-axis so the equation \(x^2 + 2x + 5 = 0\) has no roots. The graph of the quadratic equation \(y = ax^2 + bx ...