Solving polynomial inequalities- find and graph the solution set
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Let A=z(z²+7z+10)=z(z+5)(z+2)

TEST z z z+5 z+2 A
-6 (z<-5) <0 (-) <0 (-) <0 (-) <0
-3 (-5<z<-2) <0 (-) >0 (+) <0 (-) >0
-1 (-2<z<0) <0 (-) >0 (+) >0 (+) <0
1 (z>0) >0 (+) >0 (+) >0 (+) >0

The SIGN TABLE above shows the sign of A for all values of z.

Solutions: -5<z<-2 and z>0. The graph of the function with sign markings is shown below:

 

by Top Rated User (711k points)

z^3 + 7z^2 + 10z > 0

z(z^2 + 7z + 10) > 0

z(z + 2)(z + 5) > 0

Solution set is given by,

all 3 terms +ve

1 term +v e and 2 terms -ve

This can be modelled as

+   +   +   > 0  -->   z > 0   (z + 2) > 0   (z + 5) > 0 ->   z > 0

+   -   -   > 0   -->   z > 0   (z + 2) < 0   (z + 5) < 0 ->    no solution

-   +   -   > 0   -->   z < 0   (z + 2) > 0   (z + 5) < 0 ->    no solution

-   -   +   > 0   -->   z < 0   (z + 2) < 0   (z + 5) > 0 ->    -5 < z < -2

There are thus two solution sets: z > 0 and -5 < z < -2

by Level 11 User (80.9k points)

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