Domanda del libro di testo
Perform the indicated operation(s) and write the result in standard form. (2 - 3i)(1 - i) - (3 - i)(3 + i)
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 65
Solve each equation in Exercises 65–74 using the quadratic formula.
Guida verificata passo dopo passo1
Identify the coefficients in the quadratic equation \(x^2 + 8x + 15 = 0\). Here, \(a = 1\), \(b = 8\), and \(c = 15\).
Recall the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Substitute the values of \(a\), \(b\), and \(c\) into the quadratic formula: \(x = \frac{-8 \pm \sqrt{8^2 - 4 \cdot 1 \cdot 15}}{2 \cdot 1}\).
Simplify inside the square root (the discriminant): calculate \(8^2 - 4 \cdot 1 \cdot 15\) to determine the value under the square root.
Evaluate the square root and then compute the two possible values for \(x\) by using the plus and minus signs in the formula.
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Quadratic Equation
A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a ≠ 0. It represents a parabola when graphed, and its solutions are the x-values where the parabola intersects the x-axis.
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05:35
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 coefficients a, b, and c to find roots, including real and complex solutions.
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06:36Solving Quadratic Equations Using The Quadratic Formula
Discriminant
The discriminant, given by b² - 4ac, determines the nature of the roots of a quadratic equation. If positive, there are two distinct real roots; if zero, one real root; and if negative, two complex conjugate roots.
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04:11The Discriminant
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