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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 85
Capitolo 2, Problema 85

Solve each equation in Exercises 83–108 by the method of your choice. 5x2+2=11x5x^2 + 2 = 11x

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Rewrite the given equation to standard quadratic form by moving all terms to one side: \(5x^2 + 2 = 11x\) becomes \(5x^2 - 11x + 2 = 0\).
Identify the coefficients in the quadratic equation $ax^2 + bx + c = 0$: here, \(a = 5\), \(b = -11\), and \(c = 2\).
Use the quadratic formula to solve for \(x\): \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Calculate the discriminant \(\Delta = b^2 - 4ac\) to determine the nature of the roots.
Substitute the values of \(a\), \(b\), and \(c\) into the quadratic formula and simplify under the square root and the entire expression to find the solutions for \(x\).

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Quadratic Equations

A quadratic equation is a polynomial equation of degree two, generally written as ax² + bx + c = 0. Solving such equations involves finding the values of x that satisfy the equation. Recognizing the standard form is essential for applying appropriate solution methods.
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Introduction to Quadratic Equations

Rearranging Equations

Rearranging involves moving all terms to one side to set the equation equal to zero. This step is crucial for quadratic equations because it allows the equation to be expressed in standard form, enabling the use of factoring, completing the square, or the quadratic formula.
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Categorizing Linear Equations

Methods for Solving Quadratic Equations

Common methods include factoring, completing the square, and using the quadratic formula. Factoring works when the quadratic can be expressed as a product of binomials. The quadratic formula applies universally and is derived from completing the square.
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Choosing a Method to Solve Quadratics
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Domanda del libro di testo

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2/x + 1/2 = 3/4

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Domanda del libro di testo

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

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Solve each absolute value inequality. - 4|1 - x| < - 16

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Solve each polynomial equation in Exercises 86–87. 2x^4 = 50 x^2

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Domanda del libro di testo

In Exercises 59–94, solve each absolute value inequality. 3 ≤ |2x - 1|

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Domanda del libro di testo

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. ∣2x2−4∣=∣2x2∣|2x^2 - 4| = |2x^2|

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