Question

Solve the quadratic equation. $$x^{2}+12 x+20=0$$

   Solve the quadratic equation. $$x^{2}+12 x+20=0$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 12, Problem 60

Instant Answer

Solved by Expert Sonam Khatri

09/07/2020

Step 1

Step 1: First, we rewrite the given quadratic equation as follows: \[x^{2}+12 x+20=0\] Show more…

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Solve the quadratic equation. $$x^{2}+12 x+20=0$$

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Key Concepts

Discriminant

The discriminant, expressed as b² - 4ac in the context of the quadratic formula, indicates the nature and number of the roots of a quadratic equation. A positive discriminant signals two distinct real roots, zero indicates a repeated real root, and a negative discriminant implies a pair of complex conjugate roots.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac))/(2a), is a universal method for solving quadratic equations. It directly applies to any quadratic equation regardless of whether the expression factors nicely and provides the exact roots depending on the values of a, b, and c.

Zero Product Property

The zero product property states that if the product of two factors equals zero, then at least one of the factors must be zero. This property is key when utilizing factoring as a solution method for quadratic equations, as it allows for the equation to be split into simpler equations that can be solved individually.

Quadratic Equation

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 not zero. It represents parabolic relationships and is foundational in algebra for modeling various types of problems.

Factoring

Factoring involves rewriting the quadratic expression as a product of two simpler binomial expressions. This method leverages the concept that if the product of factors is zero, then at least one of the factors must be zero, making it an effective way to find the roots when the quadratic expression can be decomposed neatly.

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