In Exercises 11–12, solve each quadratic equation using the quadratic formula. Express solutions

step 1 Okie dokey, we want to find the values of x that satisfy this equation. Now, putting this out in

In Exercises 11–12, solve each quadratic equation using the...

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Key Concepts

Standard Form

The standard form of a quadratic equation is ax² + bx + c = 0. Presenting the equation in this form is important because it allows for the consistent application of solution methods such as factoring, completing the square, and especially the quadratic formula, which relies on knowing the coefficients a, b, and c.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), provides a direct method for finding the solutions (or roots) of any quadratic equation. It is derived from the process of completing the square and is particularly useful for equations that cannot be easily factored.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants and a ? 0. This form is fundamental in algebra and serves as the basis for many problem-solving techniques including graphing, factoring, and the use of the quadratic formula.

Discriminant

The discriminant is the part of the quadratic formula that lies under the square root, expressed as b² - 4ac. It reveals important information about the nature of the roots of the quadratic equation: if it is positive, there are two distinct real roots; if it is zero, there is one real repeated root; and if it is negative, the equation has two complex roots.

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