Solving Quadratics

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 ≠ 0.

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ .

The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and graphing.

The quadratic formula is $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ , used to find the solutions of a quadratic equation.

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

To factor a quadratic equation, find two numbers that multiply to $$ac$$ (the product of a and c) and add to $$b$$ . Rewrite the equation and factor by grouping.

Completing the square is a method used to convert a quadratic equation into the form $$(x - p)^2 = q$$ , making it easier to solve.

x = -7, x = -\frac{3}{2}

x = \pm 3i

The square root method involves isolating the squared term and taking the square root of both sides to find the solutions.