## RH 2 years ago When solving the polynomial inequality 4x^5 - 18x^4 + 18x^3 ≥ 0 how many graphs will you draw before you draw your final graph? A. two B. four C. five D. six

1. RH

2. DHASHNI
3. amir.sat

4x^5 - 18x^4 + 18x^3 ≥ 0 divide it by x^2 so it's 4x^3 - 18x^2 + 18x ≥ 0 for the x>0 it's 4x^2 - 18x + 18 ≥ 0 (first graph) and for the x <0 it's 4x^2 - 18x + 18 < 0 (second graph) if you draw the first graph the the impossible rations for x>0 is $\left( 0 , 1.5 \right) \cup \left( 3 , \infty \right) \cup \ { 0 , 1.5 , 3}$ but the second graph for the x<0 doesn't have any rations so the total answer is $\left( 0 , 1.5 \right) \cup \left( 3 , \infty \right) \cup \ { 0 , 1.5 , 3}$

4. RH

@amir.sat Sorry I don't understand :(

5. amir.sat

which part?

6. RH

Now I understand, so when solving the inequality, 2 graphs will be drawn before the final graph?

7. amir.sat

the point is that you divide an inequality by variable that can be negative you should separate it to two inequality one for the negative variable and one for the positive variable

8. RH

Hmm... ok

9. RH

then what would be the right answer?

10. amir.sat

all of 'em i meant the sum of each seperated graph's answer

11. RH

Sorry, I am confused:(

12. amir.sat

you separated the inequality into two inequality when you divide it by a variable i meant the answer is the sum of the separated inequality's answer

13. RH

So the right answer would be A ?

14. amir.sat

oh sorry .yes it's A i didn't see the options , i just thought it's just the questions

15. RH

No prob. Thank you a lot!!! :)

16. amir.sat

ur welcome