SOLUTION: 6x^2+8x+2 equal to / than 0 Thank you in advance! x's are variables sorry about that!can pull the 2 out but can't do anything with it..

Algebra ->  Inequalities -> SOLUTION: 6x^2+8x+2 equal to / than 0 Thank you in advance! x's are variables sorry about that!can pull the 2 out but can't do anything with it..      Log On


   

Question 851538: 6x^2+8x+2 equal to / than 0 Thank you in advance! x's are variables sorry about that!can pull the 2 out but can't do anything with it..
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean 6x%5E2%2B8x%2B2=0 ? The "... to / than..." cannot be understood. You categorized your question in "Algebra: Inequalities, trichotomy". You gave no precise inequality direction or other quality.

Simplify the numeric statement by dividing both sides by 2:
3x%5E2%2B4x%2B1=0
The roots would be critical points.
x----%28-4-sqrt%2816-4%2A3%2A1%29%29%2F%282%2A3%29
%28-4-2%29%2F%282%2A3%29
highlight%28-6%2F3%29
x-------highlight%28-2%29-----One of the critical points
AND
x-----%28-4%2B2%29%2F%282%2A3%29=highlight%28-1%2F3%29----Other critical point

The expression of the left side of the numeric statement indicates that the vertex would be a minimum, a parabola opening upward. The interval between the critical points is where the function is negative; and to the left of x=-2 and to the right of x=-1/3 the function is positive.