Question

Solve the inequality 2x^2 -x + 3 >_ 0

Answer 1

The ^2 represents exponent of 2 and >_ means greater/less than or equal to.

Possible answers are

A: x <_ -2 or x >_ 3
B: -2 <_ x <_ 3
C: No solution.
D: All Real Numbers.

Answer 2

factor \(\bf 2x^2 -x + 3\) what does it give you?

Answer 3

Do I split that into two parentheses groups?

Answer 4

yeap

Answer 5

(2x - 1) (x - 3)

Answer 6

So what now?

Answer 7

hmmm actually.... that'd give you \(\bf 2x^2-7x+3\) are you sure is \(\bf 2x^2-X+3\)?

Answer 8

well \(\bf 2x^2-x+3\)

Answer 9

So it should be reversed, some of the numbers?

Answer 10

for that doesn't factor out nicely

Answer 11

So should it be 3 and 1 reversed?

Answer 12

But that isn't part of the answer group.

Answer 13

hmmm right.. meaning is not \(\bf 2x^2-x+3\) so.... recheck your material.... you maybe missing a digit there

Answer 14

Let me see.

Answer 15

It was 2x^2 - x + 3 >_ 0

Answer 16

So I don't think I'm missing something here.

Answer 17

hmmm can you post a quick screenshot of the material?

Answer 18

\[Solve the Inequality: 2x ^{2} - x + 3 \ge 0 \]

Answer 19

With the same answers.

Answer 20

hmmm do you know how to take a screenshot? press the PrintScreen button on the keyboard, next to the F12 key
then go to Paint and paste, save and post :)

Answer 21

for \(\bf 2x^2-x+3\) the factors are rational ones, or fractions, thus

Answer 22

So that would kind of eliminate at least one of them.

Answer 23

hmmm I see... you think is no solution or the ther....hmmm

have you covered the quadratic equation?

Answer 24

Quadratic, could we walk through this one?

Answer 25

well.. if you haven't covered it, means, the exercise doesn't apply to it
or you're not expected to use it to solve it......

so... was wondering how are you meant to solve it for "x" then?

Answer 26

I've covered it, it's just not my strong point.

Answer 27

factoring is one way, simple if the factors are integers
in this case they're fractions though

Answer 28

But then again, it does mention quadratics.

Answer 29

hmm do you know what "quadratic" means?

Answer 30

It's a formula for solving equations.

Answer 31

well.... what chapter is this exercise meant to cover though?

the idea is to, give an exercise related to the section in study, if you haven't used the quadratic formula, means, you're expected to solve it differently, maybe even graphically only

Answer 32

For right now, this one is meant to solve inequalities with quadratics.

Answer 33

hmmm ok..... so you're not really expected to get the actual value..

so let's take a peek at the graph http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyeF4yLXgrMyIsImNvbG9yIjoiI0NGMEYwRiJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi01LjQ0IiwiNy41NiIsIjAuNjYwMDAwMDAwMDAwMDAwMSIsIjguNjYiXX1d

notice that graph,
notice the x-axis
notice the y-axis


so you're being asked
for what values on the x-axis, or "x"
is the graph above 0 on the y-axis

so... what do you think?

Answer 34

a parabola keeps on going endlessly btw, to the left and to the right

Answer 35

parabola, meaning the graph of the "quadratic" equation

quadratic equation = equation of 2nd degree

Answer 36

It looks like it has a positive three in it.

Answer 37

well.. .is below the 3
btw you can use the mouse to drag the graph up or down on whatever direction to view more of it
and you can use the middle mouse button to zoom in the "3" if you want
is not 3, is less than 3

Answer 38

It's between two and three.

Answer 39

more like 2.88

Answer 40

But that still isn't one of the available options.

Answer 41

hmm lememm reread
\(\bf 2x^2 -x + 3 >0\implies 2x^2 -x + 3 >{\color{blue}{ y}}\qquad
\begin{cases}
{\color{blue}{ y}}=0\\
x=?
\end{cases}\)

so.. what is "x" when "y = 0"

Answer 42

2 ?

Answer 43

anyhow, I'd make it short

from the graph, the graph over the y-axis, goes as low as 2.88 or thereabouts, right below the 3

and from that point, it goes up, on the left or right side, it goes up, never down
thus

the graph "never touches the x-axis"

because the lowest the y-value is, is about 2.88
when y= 0 is when the graph touches the x-axis