advanced functions

posted by .

Solve the inequality 12x^3 + 8x^2 <= 3x + 2. Justify your answer.

  • advanced functions -

    12x^3 + 8x^2 ≤ 3x + 2
    12x3 + 8x^2 - 3x - 2 ≤ 0

    after some trial and errors where I tried
    x = ±1, ±2, etc, I found
    x = ±1/2 and x = -2/3 give me zero

    12x3 + 8x^2 - 3x - 2 ≤ 0
    (2x-1)(2x+1)(3x+2) ≤ 0

    knowing the behaviour of
    y = 12x3 + 8x^2 - 3x - 2
    and having x-intercepts of -2/3, -1/2 and +1/2

    the solution would be
    x ≤ -2/3 OR -1/2 ≤ x ≤ 1/2

    confirmation:
    http://www.wolframalpha.com/input/?i=plot+12x3+%2B+8x%5E2+-+3x+-+2+≤+0

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra 2(check) cont..

    1)solve the inequality -3(r-11)+15>_9 my answer = r<_13 2)solve the inequality -2<4z+10<_12 my answer = -3<z<_1/2 3)solve the inequality 2x-5<_10 or 33-4x<5 my answer is x<_15/2 or <7 4)solve the inequality …
  2. math

    Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of …
  3. math 116 appendix d

    b) Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number …
  4. Algebra

    For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number …
  5. algebra

    1. You are planning to spend no more than $10,000 and no less than $8,000 on your landscaping project. a. Write an inequality that demonstrates how much money you will are willing to spend on the project. b. For the first phase of …
  6. Advanced Functions

    how do i solve this linear inequality equation x+2 divided by 2 greater than/equal to x-2 divided by 4 answer is [-10, infinity)
  7. math advanced functions grade 12

    Find the solution set to the following rational inequality, 240/x+8 > 20x/x+1
  8. Reiny and steve do this for me please

    1. Consider the functions f(x)=1/(x)+4 and g(x)=2/(x). Graph f and g on the same grid. a) Determine the points of intersection of the two functions. b) Show where f(x)<g(x). c) Solve the equation 1/(x)+4=2(x) to check your answer …
  9. math. can someone do this for me please....

    * Consider the functions f(x)=1/x +4 and g(x)=2/x. Graph f and g on the same grid. a)Determine the points of intersection of the two functions. b)Show where f(x)<g(x). c)Solve the equation 1/x +4=2/x to check your answer to part …
  10. Advanced Functions

    Solve the polynomial inequality algebraically. x^2-2x-8 ≤ 0

More Similar Questions