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Chapter 3: Q. 17 (page 171)

In problems 7-22, solve the inequality.

x2-x+1鈮�0

Short Answer

Expert verified

The given inequality has no solution.

Step by step solution

01

Step 1. Given Information

The given inequality isx2-x+1鈮�0.

02

Step 2. Find the intercepts and vertex

  • The value of f(0)=1.
  • So, the y-intercept is (0,1).
  • There are no real roots of x2-x+1=0, so, there are no x-intercepts of the curve.
  • The vertex of the parabola exists at -b2a=-(-1)2(1)=12.
  • Find the value of the function at x=12.

f(12)=(12)2-(12)+1=14-12+1=1-2+44=34

  • So, the vertex is (12,34).
03

Step 3. Plot the graph

Plot the parabola on a graph using the vertex and intercepts calculated in the previous step.

04

Step 4. Find the solution set

  • From the graph, there is no region that lies below thex-axis.
  • So, the given inequality has no solution.

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