Domanda del libro di testo
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. -2(x + 3) = -6(x + 7)
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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.6.50
Solve each quadratic equation using the zero-factor property. See Example 5.
9x² - 12x + 4 = 0
Guida verificata passo dopo passo1
Recognize that the given equation is a quadratic equation in the form $ax^{2} + bx + c = 0$, where \(a = 9\), \(b = -12\), and \(c = 4\).
Check if the quadratic can be factored easily. Notice that \(9x^{2} - 12x + 4\) is a perfect square trinomial because \(9x^{2} = (3x)^{2}\) and \(4 = 2^{2}\), and the middle term \(-12x\) equals \(2 \times 3x \times (-2)\).
Rewrite the quadratic as a square of a binomial: \((3x - 2)^{2} = 0\).
Apply the zero-factor property, which states that if a product of factors equals zero, then at least one of the factors must be zero. Here, set the factor equal to zero: \(3x - 2 = 0\).
Solve the linear equation \(3x - 2 = 0\) by isolating \(x\): add 2 to both sides and then divide both sides by 3 to find the solution 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. It represents a parabola when graphed, and its solutions are the values of x that satisfy the equation.
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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. This step is essential before applying the zero-factor property, as it breaks down the quadratic into simpler expressions that can be individually set to zero.
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Percorso guidato
6:08Factoring
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Solve each quadratic equation using the square root property. See Example 6. (3x - 1)² = 12
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