Domanda del libro di testo
Solve each quadratic equation using the zero-factor property. See Example 5. -4x² + x = -3
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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.6.47
Solve each quadratic equation using the zero-factor property. See Example 5. x² - 100 = 0
Guida verificata passo dopo passo1
Rewrite the equation in the form \(x^2 - 100 = 0\) to identify it as a difference of squares.
Recognize that \(x^2 - 100\) can be factored using the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b)\), where \(a = x\) and \(b = 10\).
Factor the equation as \((x - 10)(x + 10) = 0\).
Apply the zero-factor property, which states that if a product of two factors equals zero, then at least one of the factors must be zero. Set each factor equal to zero: \(x - 10 = 0\) and \(x + 10 = 0\).
Solve each equation separately to find the solutions for \(x\): \(x = 10\) and \(x = -10\).
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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 principle is essential for solving quadratic equations factored into binomials, allowing us to set each factor equal to zero and solve for the variable.
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Percorso guidato
6:08
Factoring
Factoring Quadratic Equations
Factoring involves rewriting a quadratic equation as a product of two binomials or simpler expressions. For example, x² - 100 can be factored using the difference of squares into (x - 10)(x + 10). Factoring simplifies the equation and prepares it for applying the zero-factor property.
Video consigliato:
Percorso guidato
6:08Factoring
Difference of Squares
The difference of squares is a special factoring formula: a² - b² = (a - b)(a + b). Recognizing this pattern helps factor expressions like x² - 100, where 100 is 10². This technique is crucial for breaking down certain quadratic equations quickly and accurately.
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Percorso guidato
4:47Sum and Difference of Tangent
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