교과서 질문
Exercises 53–60 show incomplete graphs of given polynomial functions. a) Find all the zeros of each function. b) Without using a graphing utility, draw a complete graph of the function. f(x)=3x5+2x4−15x3−10x2+12x+8
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Ch. 3 - Polynomial and Rational Functions
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
4장, 문제 59
Solve:
검증된 단계별 안내1
Start with the given equation: \(\sqrt{x} + \sqrt{x + 5} = 5\).
Isolate one of the square root terms, for example, \(\sqrt{x + 5} = 5 - \sqrt{x}\).
Square both sides of the equation to eliminate the square root on the right: \(\left(\sqrt{x + 5}\right)^2 = \left(5 - \sqrt{x}\right)^2\).
Simplify both sides: \(x + 5 = 25 - 10\sqrt{x} + x\).
Rearrange the equation to isolate the remaining square root term and then square both sides again to solve for \(x\).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Square Roots and Radicals
Square roots represent a value that, when multiplied by itself, gives the original number. Understanding how to manipulate and simplify expressions involving square roots is essential, especially when they appear in equations. Recognizing that √x denotes the principal (non-negative) root is important for solving radical equations.
추천 영상:
02:20
Imaginary Roots with the Square Root Property
Isolating and Squaring Both Sides
To solve equations involving square roots, one common method is to isolate the radical expression and then square both sides to eliminate the square root. This process can introduce extraneous solutions, so it is crucial to check all potential solutions in the original equation.
추천 영상:
03:42Linear Inequalities with Fractions & Variables on Both Sides
Solving Quadratic Equations
After squaring, the equation often becomes quadratic in form. Knowing how to solve quadratic equations using factoring, completing the square, or the quadratic formula is necessary to find the values of x. Verifying solutions against the original equation ensures only valid answers are accepted.
추천 영상:
06:08Solving Quadratic Equations by Factoring
관련 실천
교과서 질문
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x - 2)/(x + 2) ≤ 2
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교과서 질문
In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. g(x) = (2x - 4)/(x + 3)
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교과서 질문
In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. h(x) = (x^2 - 3x - 4)/(x^2 - x -6)
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교과서 질문
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation.1/(x - 3) < 1
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교과서 질문
Follow the seven steps to graph each rational function. f(x)=2x/(x2−4)
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