Chapter 4: Q. 3 (page 247)

Solve the inequality $x^{2} - 3 x < 4$ and graph the solution set.

Short Answer

Expert verified

The solution set of inequality is $(- 1, 4)$ and the graph is

Step by step solution

Step 1. Given Information

The given inequality is $x^{2} - 3 x < 4$

Step 2. Calculation

Solve the inequality by rearranging it such that the right side has 0.

$x^{2} - 3 x - 4 < 4 - 4 x^{2} - 3 x - 4 < 0$

Solve $f (0)$ to find the y-intercept.

$f (0) = {(0)}^{2} - 3 (0) - 4 = - 4$

Factorize the equation.

$(x - 4) (x + 1) = 0 x = 4, - 1$

Thus, x-intercept are $4 a n d - 1$

Step 3. Calculation

On comparing the function with the general form, we get,

$a = 1, b = - 3, c = - 4$

We will find the x- coordinate of the vertex as follows,

$\frac{- b}{2 a} = - \frac{- 3}{2} = \frac{3}{2}$

Solve $f (\frac{3}{2})$ to get the y-coordinate

$f (\frac{3}{2}) = {(\frac{3}{2})}^{2} - 3 (\frac{3}{2}) - 4 = \frac{9}{4} - \frac{9}{2} - 4 = - \frac{25}{4}$

Graph the function by plotting all the points.

And the solution set is $\{x | - 1 < x < 4\}$

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Solve the inequality $x^{2} - 3 x < 4$ and graph the solution set.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Calculation

One App. One Place for Learning.

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Solve the inequalityx2-3x<4and graph the solution set.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Theoretical and Mathematical Physics

Pure Maths

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Study anywhere. Anytime. Across all devices.

Solve the inequality $x^{2} - 3 x < 4$ and graph the solution set.