Domanda del libro di testo
Solve each quadratic equation using the square root property. See Example 6. (3x - 1)² = 12
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema R.6.42
Solve each quadratic equation using the zero-factor property. See Example 5.
x² + 2x - 8 = 0
Guida verificata passo dopo passo1
Start with the quadratic equation given: \(x^{2} + 2x - 8 = 0\).
Factor the quadratic expression on the left side. Look for two numbers that multiply to \(-8\) and add to \(2\).
Rewrite the quadratic as a product of two binomials: \((x + a)(x + b) = 0\), where \(a\) and \(b\) are the numbers found in the previous step.
Apply the zero-factor property, which states that if $AB = 0$, then either \(A = 0\) or \(B = 0\). Set each binomial equal to zero: \(x + a = 0\) and \(x + b = 0\).
Solve each linear equation for \(x\) to find the solutions to the original quadratic equation.
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Quadratic Equations
A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a ≠ 0. It represents a parabola when graphed and can have zero, one, or two real solutions depending on the discriminant.
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Percorso guidato
5:35
Introduction to Quadratic Equations
Zero-Factor Property
The zero-factor property states that if the product of two factors equals zero, then at least one of the factors must be zero. This property is used to solve quadratic equations by factoring them into binomials set equal to zero.
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Percorso guidato
6:08Factoring
Factoring Quadratic Expressions
Factoring involves rewriting a quadratic expression as a product of two binomials. For example, x² + 2x - 8 factors into (x + 4)(x - 2). This step is essential before applying the zero-factor property to find the solutions.
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Percorso guidato
6:08Factoring
Pratica correlata
Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7.
x² - x - 1 = 0
712
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Domanda del libro di testo
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. -2x - 2 ≤ 1 + x
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Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 2x - 2 = 0
74
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Domanda del libro di testo
Solve each quadratic equation using the square root property. See Example 6. x² = 16
57
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Domanda del libro di testo
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. 5x +2 ≤ -48
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