교과서 질문
Solve each problem. A comprehensive graph of ƒ(x)=x4-7x3+18x2-22x+12 is shown in the two screens, along with displays of the two real zeros. Find the two remaining nonreal complex zeros.
50
views
Ch. 3 - Polynomial and Rational Functions
Lial13th EditionCollege AlgebraISBN: 9780136881063
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
TOC.tableOfContents
4장, 문제 92
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. x2 - 9x + 20 < 0
검증된 단계별 안내1
Start by rewriting the inequality: \(x^{2} - 9x + 20 < 0\).
Factor the quadratic expression on the left side. Look for two numbers that multiply to \(20\) and add to \(-9\). This gives: \((x - 4)(x - 5) < 0\).
Determine the critical points by setting each factor equal to zero: \(x - 4 = 0\) and \(x - 5 = 0\), which gives \(x = 4\) and \(x = 5\).
Use these critical points to divide the number line into three intervals: \((-\infty, 4)\), \((4, 5)\), and \((5, \infty)\). Test a value from each interval in the inequality \((x - 4)(x - 5) < 0\) to see where the product is negative.
Based on the test results, write the solution set in interval notation, including only the intervals where the inequality holds true.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
9m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Solving Quadratic Inequalities
Solving quadratic inequalities involves finding the values of the variable that make the quadratic expression less than, greater than, or equal to zero. This typically requires factoring the quadratic, identifying critical points, and testing intervals to determine where the inequality holds true.
추천 영상:
04:03
Choosing a Method to Solve Quadratics
Factoring Quadratic Expressions
Factoring is the process of expressing a quadratic polynomial as a product of two binomials. For example, x² - 9x + 20 factors into (x - 4)(x - 5). Factoring helps find the roots of the quadratic, which are essential for determining the intervals to test in inequalities.
추천 영상:
06:08Solving Quadratic Equations by Factoring
Interval Notation
Interval notation is a way to represent sets of numbers on the number line. It uses parentheses and brackets to indicate open or closed intervals, respectively. For inequalities, interval notation concisely expresses the solution set where the inequality is true.
추천 영상:
05:18Interval Notation
관련 실천
교과서 질문
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. 2x2 - 9x ≥ 18
518
views
교과서 질문
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function.
497
views
교과서 질문
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function.
393
views
교과서 질문
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=9x6-7x4+8x2+x+6
346
views
교과서 질문
Use the technique described in Exercises 87–90 to solve each inequality. Write the solution set in interval notation. x2 - x - 6 < 0
493
views