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91Ó°ÊÓ

In the following exercises, solve each inequality algebraically and write any solution in interval notation:

x2-2x+4≥0

Short Answer

Expert verified

The solution of the inequality is-∞ , ∞ .

Step by step solution

01

Step 1. Given information.

We have:

x2-2x+4≥0

02

Step 2. Solve the inequality.    

Change the sign ≥with 0and solve by quadratic formula.

x2-2x+4=0For a quadratic equation of the form ax2+bx+c=0 the solutions are x1, 2=-b±b2-4ac2aFor a=1, b=-2, c=4x1, 2=--2±-22-4· 1· 42· 1x1, 2=--2± 23i2· 1

No real solution.

The equation is true for any value of x.

Therefore, there are infinitely many solutions.

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