express the following equation 2

Question

Express the following equation, using Ω Ο or Θ notation
|3x^5 -4x^4 +3x^3 +2x^2 +5x +12| ≤ 12|x^5 |

Answer 1

Given equation

|3x^5 -4x^4 +3x^3 +2x^2 + 5x +12| ≤ 12|x^5 | Subtract 12 |x^5| from both sides

|3x^5 -4x^4 +3x^3 +2x^2 + 5x +12| - 12|x^5 | ≤ 0 Simplify

|3x^5 -4x^4 +3x^3 +2x^2 + 5x +12 - 12x^5 | ≤ 0

|-9x^5 -4x^4 +3x^3 +2x^2 + 5x +12| ≤ 0

Graph of function: θ(x) = |-9x^5 -4x^4 +3x^3 +2x^2 + 5x +12|

has only positive values. Therefore, solution of inequality  and function

|-9x^5 -4x^4 +3x^3 +2x^2 + 5x +12| ≤ 0  does not exist.

I hope this helps.

Sincerely,

Shailesh (Sky) Kadakia, Expert Math Tutor