Chapter 3: Q. 17 (page 171)

In problems 7-22, solve the inequality.
$x^{2} - x + 1 \leq 0$

Short Answer

Expert verified

The given inequality has no solution.

Step by step solution

Step 1. Given Information

The given inequality is $x^{2} - x + 1 \leq 0$ .

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 $x^{2} - x + 1 = 0$ , so, there are no x-intercepts of the curve.
The vertex of the parabola exists at $\frac{- b}{2 a} = \frac{- (- 1)}{2 (1)} = \frac{1}{2}$ .
Find the value of the function at $x = \frac{1}{2}$ .

$\begin{array}{rcl} f (\frac{1}{2}) & = & {(\frac{1}{2})}^{2} - (\frac{1}{2}) + 1 \\ = & \frac{1}{4} - \frac{1}{2} + 1 \\ = & \frac{1 - 2 + 4}{4} \\ = & \frac{3}{4} \end{array}$

So, the vertex is $(\frac{1}{2}, \frac{3}{4})$ .

Step 3. Plot the graph

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

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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In problems 7-22, solve the inequality.
$x^{2} - x + 1 \leq 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the intercepts and vertex

Step 3. Plot the graph

Step 4. Find the solution set

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In problems 7-22, solve the inequality. x2-x+1≤0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the intercepts and vertex

Step 3. Plot the graph

Step 4. Find the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

In problems 7-22, solve the inequality.
$x^{2} - x + 1 \leq 0$