step 1 We've got 2x squared minus 7x plus 5, and we want to factor it. So to start, we're going to repl

2 x^2-7 x+5 | Numerade

Name: Problem 19, Chapter 6: Beginning and Intermediate Algebra
Uploaded: 2020-03-08T17:32:58-08:00
Duration: 1 min 34 s
Channel: Kimberly Moon
Description: 2 x^2-7 x+5

Key Concepts

Quadratic Expression

A quadratic expression is a second-degree polynomial typically written in the form ax² + bx + c, where a, b, and c are constants and a ? 0. It represents a parabola when graphed and is a fundamental object in algebra, with applications ranging from solving equations to modeling physical phenomena.

Standard Form

The standard form of a quadratic expression is ax² + bx + c. Presenting a quadratic in this form allows for easy identification of its coefficients, which are essential for analyzing properties of the expression such as its vertex, axis of symmetry, and methods for solving it.

Factorization

Factorization involves rewriting a quadratic expression as the product of two binomials. This process is useful for solving quadratic equations, simplifying expressions, and understanding the roots of the quadratic. It often requires identifying two numbers that simultaneously satisfy the relationships dictated by the coefficients of the quadratic.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac))/(2a), provides a method for finding the roots of any quadratic equation ax² + bx + c = 0. It is particularly helpful when the quadratic expression does not factor nicely, allowing for the computation of precise solutions regardless of the coefficients involved.

Discriminant

The discriminant, given by b² - 4ac, is a key component of the quadratic formula that determines the nature of the roots of a quadratic equation. A positive discriminant indicates two distinct real roots, zero indicates one real repeated root, and a negative discriminant indicates two complex conjugate roots.

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