Question

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

Answer 1

Please help! :(

Answer 2

http://www.wolframalpha.com/input/?i=4x%5E5+-+18x%5E4+%2B+18x%5E3+%E2%89%A5+0&dataset=

Answer 3

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 \[\left( 0 , 1.5 \right) \cup \left( 3 , \infty \right) \cup \ { 0 , 1.5 , 3}\]

Answer 4

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

Answer 5

which part?

Answer 6

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

Answer 7

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

Answer 8

Hmm... ok

Answer 9

then what would be the right answer?

Answer 10

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

Answer 11

Sorry, I am confused:(

Answer 12

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

Answer 13

So the right answer would be A ?

Answer 14

oh sorry .yes it's A

i didn't see the options , i just thought it's just the questions

Answer 15

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

Answer 16

ur welcome