step 1 To solve the equation, first I need to factor. So I know I have z times z, and I'm looking for t

Z^2+4 z-72=0 | Numerade

Name: Problem 36, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-07-13T14:00:30-08:00
Duration: 37 s
Channel: Kristen Karbon
Description: z^2+4 z-72=0

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Key Concepts

Discriminant

The discriminant, found inside the quadratic formula as b² - 4ac, determines the nature of the roots of a quadratic equation. A positive discriminant indicates two distinct real roots, zero indicates a repeated real root, and a negative discriminant indicates two complex conjugate roots.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in a single variable, typically expressed in the form ax² + bx + c = 0. It is fundamental in algebra and arises in various applications such as physics, engineering, and economics. The key task is to find the two solutions (roots) of the equation, which may be real or complex.

Factoring

Factoring is a method used to solve quadratic equations by rewriting the quadratic expression as a product of two linear factors. If the quadratic can be factored easily, setting each factor equal to zero (using the Zero Product Property) provides the solutions to the equation.

Quadratic Formula

The quadratic formula is a universal method for solving any quadratic equation. It is derived from completing the square and is given by z = (-b ± ?(b² - 4ac)) / (2a). This formula is particularly useful when the quadratic does not factor neatly.

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