Quadratic Formula

The Quadratic Formula is used to find the solutions of a quadratic equation in the form $$ax^2 + bx + c = 0$$ . It is given by $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

The discriminant, given by $$D = b^2 - 4ac$$ , indicates the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root (a repeated root); if D < 0, there are two complex roots.

The solutions are $$x = 2, -3$$ .

The solutions are $$x = -1, -3$$ .

The solutions are $$x = 3 \pm \sqrt{5}$$ .

To use the quadratic formula, rearrange the equation to the standard form $$ax^2 + bx + c = 0$$ .

In the quadratic formula, $$a$$ is the coefficient of $$x^2$$ , $$b$$ is the coefficient of $$x$$ , and $$c$$ is the constant term. They determine the shape and position of the parabola represented by the quadratic equation.

The solutions are $$x = \frac{7 \pm \sqrt{169}}{18}$$ .

The solutions are $$m = 2, -3$$ .

A quadratic equation is a polynomial equation of degree 2, typically in the form $$ax^2 + bx + c = 0$$ , where $$a, b,$$ and $$c$$ are constants and $$a \neq 0$$ .