Explanation Procedure used: Solving a Quadratic inequality algebraically: 1. Write an equivalent inequality with 0 on one side and with the function f ( x ) on the other side. 2. Solve f ( x ) = 0 . 3. Create a sign diagram that uses the solution from step 2 to divide the number line into intervals. Pick a test value in each interval and determine whether f ( x ) is positive or negative in that interval to create a sign diagram. 4. Identify the intervals that satisfy the inequality in step 1. The values of x that define these intervals are solutions to the original inequality. Calculation: Rewrite the given inequality as 2 x 2 + 5 x − 3 ≥ 0 . First obtain the values of x such that 2 x 2 + 5 x − 3 = 0 . Factorize the above equation to find the values of x . 2 x 2 − x + 6 x − 3 = 0 x ( 2 x − 1 ) + 3 ( 2 x − 1 ) = 0 ( x + 3 ) ( 2 x − 1 ) = 0 ( x + 3 ) ( x − 1 2 ) = 0 Now solve ( x + 3 ) ( x − 1 2 ) = 0 and find the value of x . Thus, the values of x is x = − 3 and x = 1 2 . These values divide the number line into three intervals: the numbers less than − 3 , the numbers between − 3 and 1 2 , and the numbers greater than 1 2

College Algebra in Context with Integrated Review and Worksheets Plus MyLab Math with Pearson eText-- Access Card Package

1st Edition

ISBN: 9780134380155

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4, Problem 32RE

To determine

To solve: The inequality 2x2+5x≥3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 31RE

Chapter 4, Problem 33RE

Students have asked these similar questions

Q5*) Write down an immediate first integral for the Euler-Lagrange equation for the integral I = = F(x, y, y″) dx. Hence write down a first integral of the Euler-Lagrange equation for the integral I 1 = √(xy ² + x³y²) dx. Find the general solution of this ordinary differential equation, seeking first the complementary function and then the particular integral. (Hint: the ODE is of homogeneous degree. And, for the particular integral, try functions proportional to log x.)

You are provided with three 2D data points, p1, p2 and p3. Solving A C = B for C provides youwith the coefficients of a natural cubic spline curve that interpolates these points.Additionally, you have been given A and B, but some elements are missing. Moreover, the last two rowsof A are entirely absent. Your task is to determine and fill in the missing elements. For the last two rows,enforce a zero tangent at the beginning (in p1) and a not-a-knot boundary condition in p2. The matricesA and B are given as follows:Explain how to find the entries of A and B . How would you adapt these matrices if the data pointswere 3D? What if your spline should go through five data points? How many “extra rows” would there thenbe (with “extra” meaning “in addition to securing C2-continuity”)?

Q2*) In question P3 we showed that a minimal surface of revolution is given by revolution (about the x-axis) of the catenary, with equation y = C cosh ((x – B)/C). - (a) Suppose, without loss of generality, that the catenary passes through the initial point P = (x1,y1) = (0, 1). First deduce an expression for the one-parameter family of catenaries passing through point P. Next calculate the value of x at which y takes its minimum value. By using the inequality cosh > √2 (you might like to think about how to prove this), show that there are points Q for which it is impossible to find a catenary passing through both P and Q. In particular, show that it is impossible to find a catenary joining the points (0, 1) and (2, 1). (b) A minimal surface of revolution can be realised experimentally by soap films attached to circular wire frames (see this link and this link for examples). The physical reason for this is that the surface tension, which is proportional to the area, is being minimised.…

Chapter 4 Solutions

College Algebra in Context with Integrated Review and Worksheets Plus MyLab Math with Pearson eText-- Access Card Package

Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The inequality 2 x 2 + 5 x ≥ 3 .

Solution Summary: The author explains how to solve a quadratic inequality algebraically: write an equivalent inequality with 0 on one side and with the function f(x) on the other side.

Videos

To solve: The inequality 2x2+5x≥3.

Want to see the full answer?

Chapter 4 Solutions