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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 83
Capitolo 2, Problema 83

Solve each equation in Exercises 83–108 by the method of your choice. 2x2 - x = 1

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Rewrite the equation in standard quadratic form by moving all terms to one side of the equation: 2x^2 - x - 1 = 0.
Identify the coefficients of the quadratic equation in the form ax^2 + bx + c = 0. Here, a = 2, b = -1, and c = -1.
Choose a method to solve the quadratic equation. For example, you can use the quadratic formula: x = \(\frac{-b \pm \sqrt{b^2 - 4ac}\)}{2a}.
Substitute the values of a, b, and c into the quadratic formula: x = \(\frac{-(-1) \pm \sqrt{(-1)^2 - 4(2)(-1)}\)}{2(2)}.
Simplify the expression under the square root (the discriminant) and then simplify the entire formula to find the two possible solutions for x.

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Quadratic Equations

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. These equations can be solved using various methods, including factoring, completing the square, or applying the quadratic formula. Understanding the standard form and properties of quadratic equations is essential for solving them effectively.
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Introduction to Quadratic Equations

Factoring

Factoring involves rewriting an expression as a product of its factors. For quadratic equations, this often means expressing the equation in the form (px + q)(rx + s) = 0. This method is particularly useful when the quadratic can be easily factored, allowing for straightforward solutions by setting each factor equal to zero.
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The Quadratic Formula

The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), provides a method to find the roots of any quadratic equation. It is derived from completing the square and is applicable even when the equation cannot be factored easily. Understanding how to apply this formula is crucial for solving quadratic equations, especially when dealing with complex or irrational solutions.
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Solving Quadratic Equations Using The Quadratic Formula
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