Domanda del libro di testo
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7
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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 77
In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.
Guida verificata passo dopo passo1
Identify the coefficients in the quadratic equation \(2x^2 - 11x + 3 = 0\). Here, \(a = 2\), \(b = -11\), and \(c = 3\).
Recall the formula for the discriminant: \(\Delta = b^2 - 4ac\).
Substitute the values of \(a\), \(b\), and \(c\) into the discriminant formula: \(\Delta = (-11)^2 - 4 \times 2 \times 3\).
Simplify the expression to find the value of the discriminant (do not calculate the final number yet).
Use the value of the discriminant to determine the number and type of solutions: if \(\Delta > 0\), there are two distinct real solutions; if \(\Delta = 0\), there is one real solution; if \(\Delta < 0\), there are two complex solutions.
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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 can have zero, one, or two real solutions depending on its coefficients.
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05:35
Introduction to Quadratic Equations
Discriminant
The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature and number of solutions of a quadratic equation: if positive, two distinct real solutions; if zero, one real repeated solution; if negative, two complex solutions.
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04:11The Discriminant
Types of Solutions of Quadratic Equations
The solutions of a quadratic equation can be real or complex. Based on the discriminant, the equation may have two distinct real roots, one repeated real root, or two complex conjugate roots. Understanding these types helps in interpreting the behavior of the quadratic function.
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05:35Introduction to Quadratic Equations
Pratica correlata
Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. |3 - (2/3)x| > 5
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Domanda del libro di testo
Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).
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Domanda del libro di testo
The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|
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Domanda del libro di testo
Solve each equation by the method of your choice.
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Domanda del libro di testo
Solve each equation by the method of your choice.
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