Understanding and Solving Quadratics
A quadratic equation in one variable follows the standard form Ax² + Bx + C = 0, where A, B, and C are constants. When we solve these equations, we're looking for roots (also called zeros) - the values that make the equation equal to zero.
There are three main methods to solve quadratics: factoring, completing the square, and using the quadratic formula. To choose the right method, calculate the discriminant which reveals important information about your solutions. When the discriminant is positive, you'll have two real solutions; negative means two imaginary solutions; zero indicates exactly one solution.
When factoring quadratics, first set the equation to zero, then find two numbers that both add up to B and multiply to give A×C. This allows you to rewrite the middle term, group terms effectively, and then find your solution by setting each factor equal to zero.
Pro Tip: If the discriminant is a perfect square, the quadratic is likely factorable - making the factoring method your fastest approach!
