Textbook Question
Solve each quadratic equation using the quadratic formula. See Example 7.
x² - x - 1 = 0
Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- 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
Chapter 1, Problem R.6.43
Solve each quadratic equation using the zero-factor property. See Example 5. 5x² - 3x - 2 = 0
Verified step by step guidance1
Start with the quadratic equation: \(5x^{2} - 3x - 2 = 0\).
Factor the quadratic expression on the left side. Look for two numbers that multiply to \(5 \times (-2) = -10\) and add to \(-3\).
Rewrite the middle term \(-3x\) using the two numbers found, then group terms to factor by grouping.
Apply the zero-factor property, which states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\). Set each factor equal to zero.
Solve each resulting linear equation for \(x\) to find the solutions to the quadratic equation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Equations
A quadratic equation is a polynomial equation of degree two, generally written as ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. Solving quadratic equations involves finding the values of x that satisfy the equation.
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Introduction to Quadratic Equations
Factoring Quadratic Expressions
Factoring involves rewriting a quadratic expression as a product of two binomials. This process simplifies solving the equation by breaking it down into simpler linear factors, which can then be set to zero to find the roots.
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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 property is used to solve equations by setting each factor equal to zero and solving for the variable.
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6:08Factoring
Related Practice
Textbook Question
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 6x = -7
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Textbook Question
Solve each inequality. Give the solution set using interval notation. See Example 10. -9 ≤ x + 5 ≤ 15
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Textbook Question
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 4(2x + 7) = 2x + 22 + 3(2x + 2)
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Textbook Question
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 4x + 3 = 0
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Textbook Question
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. 4x + 7 ———— ≤ 2x + 5 -3
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