Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7. -2x² + 4x + 3 = 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.6.61
Solve each quadratic equation using the quadratic formula. See Example 7. 2x² - x - 28 = 0
Guida verificata passo dopo passo1
Identify the coefficients in the quadratic equation \(2x^{2} - x - 28 = 0\). Here, \(a = 2\), \(b = -1\), and \(c = -28\).
Recall the quadratic formula: \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\).
Calculate the discriminant \(\Delta = b^{2} - 4ac\) by substituting the values: \(\Delta = (-1)^{2} - 4 \times 2 \times (-28)\).
Evaluate the square root of the discriminant, \(\sqrt{\Delta}\), to determine the nature of the roots (real and distinct, real and equal, or complex).
Substitute \(b\), \(\sqrt{\Delta}\), and \(a\) into the quadratic formula to write the two possible solutions for \(x\): \(x = \frac{-b + \sqrt{\Delta}}{2a}\) and \(x = \frac{-b - \sqrt{\Delta}}{2a}\).
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Quadratic Equation
A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. It represents a parabola when graphed and typically has two solutions, which can be real or complex.
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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 calculate the roots, including complex roots when the discriminant is negative.
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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 repeated root; and if Δ < 0, two complex conjugate roots.
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