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Chapter 3: Q. 41 (page 172)

Explain why the inequality x2+x+1>0has all real numbers as the solution set.

Short Answer

Expert verified
  • The entire curve lies above the x-axis.
  • So, all the values in the domain of the function are the solution of the given inequality.

Step by step solution

01

Step 1. Given Information

The given inequality isx2+x+1>0.

02

Step 2. Find the Intercepts

  • Consider the function f(x)=x2+x+1.
  • The function cannot be factored further.
  • There are no x-intercepts of the curve.
  • The value off(0) is 1.
  • So, the y-intercept is 1.
  • This implies that the entire curve lies above the x-axis.
  • So, all the values in the domain of the function are the solution of the given inequality.

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