step 1 According to the question we have given equation is z square plus 6 z plus 9 is equal to 0. Firs

Solve. z^2+6 z+9=0

Name: Problem 32, Chapter 5: Intermediate Algebra : Concepts and Applications
Uploaded: 2020-07-18T11:44:21-08:00
Duration: 50 s
Channel: Ankit Gupta
Description: Solve. z^2+6 z+9=0

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Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a is non-zero. Solving such equations is fundamental in algebra, as they frequently appear in various mathematical and real-world contexts.

Factoring

Factoring is a common method used to solve quadratic equations by rewriting the quadratic expression as a product of simpler expressions, typically two linear factors. This process simplifies the task of finding the roots of the equation by applying the zero-product property.

Perfect Square Trinomials

A perfect square trinomial is a special type of quadratic expression that can be represented as the square of a binomial, such as (x + d)². Recognizing a perfect square trinomial allows for a straightforward solution, as it implies the quadratic has a repeated root or a root with multiplicity two.

Multiplicity of Roots

Multiplicity refers to the number of times a particular solution appears as a root of the equation. In the context of quadratics, when the equation factors into the square of a linear term, the sole solution is said to have a multiplicity of two, meaning it is a double or repeated root.

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