Solve by (a) Completing the square (b) Using the quadratic formula 6 x^2+11 x-10=0

Name: Problem 39, Chapter 9: Algebra Form and Function
Uploaded: 2022-04-07T16:34:09-08:00
Duration: 3 min 45 s
Channel: Alison Rodriguez
Description: Solve by (a) Completing the square (b) Using the quadratic formula 6 x^2+11 x-10=0

step 1 The first process we're going to take is by completing the square. So I get 6x squared plus 11x

Solve by (a) Completing the square (b) Using the quadratic...

Key Concepts

Discriminant

The discriminant is the part of the quadratic formula found under the square root, b² - 4ac, which determines the nature of the roots of the quadratic equation. A positive discriminant indicates two distinct real solutions, a zero discriminant indicates one real solution, and a negative discriminant indicates two complex solutions.

Quadratic Formula

The quadratic formula is a universal method for solving quadratic equations. Derived from the process of completing the square, it states that the solutions of ax² + bx + c = 0 can be found using the formula x = (-b ± ?(b² - 4ac)) / (2a). This formula is particularly useful when the quadratic cannot be easily factored.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable of the form ax² + bx + c = 0, where a, b, and c are constants and a is not zero. Such equations typically have two solutions, which can be real or complex, and they serve as a foundational concept in algebra.

Completing the Square

Completing the square is a method used to solve quadratic equations by rewriting the quadratic expression as a perfect square trinomial plus or minus a constant. This technique transforms the equation into a form that is easier to solve by isolating the variable, and it also provides insight into the vertex form of a quadratic function.