Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7.
x² - x - 1 = 0
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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.6.45
Solve each quadratic equation using the zero-factor property. See Example 5. -4x² + x = -3
Guida verificata passo dopo passo1
First, rewrite the equation so that one side equals zero. Start with the given equation: \(-4x^{2} + x = -3\). Add 3 to both sides to get: \(-4x^{2} + x + 3 = 0\).
Next, multiply the entire equation by -1 to make the leading coefficient positive, which often makes factoring easier: \(4x^{2} - x - 3 = 0\).
Now, factor the quadratic expression \(4x^{2} - x - 3\). Look for two numbers that multiply to \(4 \times (-3) = -12\) and add to \(-1\) (the coefficient of \(x\)).
Use these numbers to split the middle term and factor by grouping. This will give you two binomials multiplied together, such as \((ax + b)(cx + d) = 0\).
Finally, apply the zero-factor property: set each factor equal to zero, $ax + b = 0$ and $cx + d = 0$, then solve each equation for \(x\) to find the solutions.
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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 solving it means finding 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 is zero, then at least one of the factors must be zero. This property is used to solve quadratic equations by factoring them into two binomials set equal to zero.
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Percorso guidato
6:08Factoring
Rearranging Equations to Standard Form
Before applying the zero-factor property, the quadratic equation must be rearranged into standard form (ax² + bx + c = 0). This involves moving all terms to one side of the equation to set it equal to zero.
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Percorso guidato
6:50Convert Equations from Polar to Rectangular
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