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.6.59
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 4x + 3 = 0
Guida verificata passo dopo passo1
Identify the coefficients from the quadratic equation \(x^2 - 4x + 3 = 0\). Here, \(a = 1\), \(b = -4\), and \(c = 3\).
Recall the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Calculate the discriminant \(\Delta = b^2 - 4ac\). Substitute the values: \(\Delta = (-4)^2 - 4 \times 1 \times 3\).
Evaluate the square root of the discriminant: \(\sqrt{\Delta}\), which will be used in the formula.
Substitute \(b\), \(a\), and \(\sqrt{\Delta}\) into the quadratic formula to find the two possible values of \(x\): \(x = \frac{-(-4) \pm \sqrt{\Delta}}{2 \times 1}\).
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Quadratic Equation
A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. It represents a parabola when graphed and has up to two real or complex solutions.
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Percorso guidato
5:35
Introduction to Quadratic Equations
Quadratic Formula
The quadratic formula x = (-b ± √(b² - 4ac)) / (2a) provides the solutions to any quadratic equation ax² + bx + c = 0. It uses the coefficients a, b, and c to find the roots, including real and complex solutions.
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Percorso guidato
6:36Quadratic Formula
Discriminant
The discriminant, given by Δ = b² - 4ac, determines the nature of the roots of a quadratic equation. If Δ > 0, there are two distinct real roots; if Δ = 0, one real root; and if Δ < 0, two complex conjugate roots.
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