Domanda del libro di testo
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the ordered pairs (- 2, 2), (0, 0), and (2, 2) to graph a straight line.
147
views
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 70
Solve each equation using the quadratic formula.
Guida verificata passo dopo passo1
Rewrite the given equation in standard quadratic form $ax^2 + bx + c = 0$. Start by moving all terms to one side: \(2x^2 + 4x - 3 = 0\).
Identify the coefficients \(a\), \(b\), and \(c\) from the quadratic equation. Here, \(a = 2\), \(b = 4\), and \(c = -3\).
Recall the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). This formula will help find the roots of the quadratic equation.
Calculate the discriminant \(\Delta = b^2 - 4ac\) by substituting the values of \(a\), \(b\), and \(c\): \(\Delta = 4^2 - 4 \times 2 \times (-3)\).
Substitute the values of \(a\), \(b\), and the discriminant \(\Delta\) into the quadratic formula to express the solutions for \(x\): \(x = \frac{-4 \pm \sqrt{\Delta}}{2 \times 2}\).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Quadratic Equation Standard Form
A quadratic equation must be written in the standard form ax² + bx + c = 0 before applying the quadratic formula. This involves rearranging all terms to one side of the equation so that the other side equals zero, allowing identification of coefficients a, b, and c.
Video consigliato:
04:34
Converting Standard Form to Vertex Form
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 real and complex solutions depending on the discriminant.
Video consigliato:
06:36Solving Quadratic Equations Using The Quadratic Formula
Discriminant and Nature of Roots
The discriminant, given by b² - 4ac, determines the type of 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. This helps predict the solution's nature before calculation.
Video consigliato:
04:11The Discriminant
Pratica correlata
Domanda del libro di testo
Find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5
782
views
Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. |x| > 3
745
views
Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. |x - 1| ≥ 2
772
views
Domanda del libro di testo
Evaluate x2 - 2x + 2 for x = 1 + i.
960
views
Domanda del libro di testo
In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 7|5x| + 2 = 16
787
views