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Chapter 4: Q. 45 (page 246)

Solve each inequality. Graph the solution set.

x2-8x+12x2-16>0

Short Answer

Expert verified

The real zeroes of the function are 6, 2 , 4 and -4and the graph is

Step by step solution

01

Step 1. Given Information 

The given inequality isx2-8x+12x2-16>0

02

Step 2. Calculation 

The inequality is already in a form with zero on the right side.

Solve the given inequality by finding the real zeroes of the numerator and denominator.

x2-8x+12=0(x-6)(x-2)=0x=6,2

And

x2-16=0x2=16x=卤4

Thus, real zeroes of the function are 6, 2, 4 and-4

03

Step 3. Graph 

Construct the table by using a number from each interval to check whether the function is positive or negative.

Thus, the solution set is x|x<-4or2<x<4orx>6

And the solution set can be graphed as

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