Solve each inequality. Express in interval notation.
2x^2+6x less than/equal to 0.

Question

Solve each inequality.  Express in interval notation.
2x^2+6x less than/equal to 0.

amistre64 · Answer

between its roots id hope

amistre64 · Answer

2x(x+3); so between -3 and 0

turingtest · Answer

$$2x^2+6x \le 0$$$$2x(x+3)\le0$$$$x \le 0$$$$x \le -3$$since the limiting factor is the second one:$$x≤−3\rightarrow(-\infty,-3]$$

anonymous · Answer

So you don't do anything with the $$x \le 0$$

turingtest · Answer

no because we know that x cannot be greater than -3. All the above says is that x is AT MOST 0. The other statement says that x is AT MOST -3.
So the fact that$$x \le -3$$implies that $$x \le 0$$

anonymous · Answer

ok.  Thanks

amistre64 · Answer

spose x = -10

2(-10)^2+6(-10)

2(100) - 60 is not less than zero so x <-3 doesnt work

amistre64 · Answer

the interval should be:  [-3,0]

amistre64 · Answer

lets try x=-4

2(-4)^2+6(-4)

2(16)-24

32-24 is greater than 0

amistre64 · Answer

graph wise, a parabola curves so that at best there is only a distinct section that is below the x axis

amistre64 · Answer

to say that it is below the x axis from -3 to -infinity is not accurate to be polite :)

amistre64 · Answer

http://www.wolframalpha.com/input/?i=2x^2%2B6x as you can see from the graph, it is equal to or less than zero from -3 to 0