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Chapter 4: Q. 3 (page 247)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information

The given inequality isx2-3x<4

02

Step 2. Calculation

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

x2-3x-4<4-4x2-3x-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)=0x=4,-1

Thus, x-intercept are4and-1

03

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,

-b2a=--32=32

Solve f(32)to get the y-coordinate

f(32)=(32)2-3(32)-4=94-92-4=-254

Graph the function by plotting all the points.

And the solution set isx|-1<x<4

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