If I can't factor a quadratic equation what will I do??

$\displaystyle x^2+2x+7\ge 0$

I don't know the latex for this.. thanks. I tried extracting the roots but it turned out as square root of a negative number?? Am I in the right track?

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- Mar 23rd 2009, 05:15 AMprincess_21[SOLVED] help
If I can't factor a quadratic equation what will I do??

$\displaystyle x^2+2x+7\ge 0$

I don't know the latex for this.. thanks. I tried extracting the roots but it turned out as square root of a negative number?? Am I in the right track? - Mar 23rd 2009, 05:30 AMskeeter
- Mar 23rd 2009, 05:32 AMprincess_21
- Mar 23rd 2009, 05:44 AMSirNostalgic
This means theres no intersection with the x-axis. if you simply need to sketch the graph find the turning point of the quadratic $\displaystyle \frac{d(y)}{d(x)} = 0$ should give you the X-coordinate of the turning point. Put that X-coordinate value into the non-differentiated equation and you'll get your Y-coordinate of the turning point

- Mar 23rd 2009, 05:49 AMprincess_21
- Mar 23rd 2009, 05:50 AMSirNostalgic
$\displaystyle x^2+2x+7$

$\displaystyle \frac{d(y)}{d(x)} = 2x+2$

$\displaystyle \frac{d(y)}{d(x)} = 0 $

$\displaystyle 2x+2 = 0$

$\displaystyle 2x = -2$

$\displaystyle x = -1$

x = -1 is the x-coordinate of the Turning point, plug into the original equation for the Y-value of this Turning point

$\displaystyle x^2+2x+7 (x= -1)

$

$\displaystyle (-1)^2 +2(-1) +7 $

= 6

Coordinates of Turning point (-1,6) I'm guessing this is a minimum :p

i swear to god my computer pasted what i wrote twice. What in gods name happened there lol - Mar 23rd 2009, 05:59 AMstapel
**Graph the quadratic**. Look at the picture. Look at the inequality.

You are asked to find the x-values for which the quadratic is at or above the x-axis. What does the picture show you?

(Wink) - Mar 23rd 2009, 06:06 AMprincess_21
- Mar 23rd 2009, 06:31 AMstapel
If the various worked examples in the lesson (provided in the link) were not sufficiently helpful, then try studying a few more

**online lessons**. (I'm assuming you understand the x,y-plane and how to graph linear equations.)

Once you've learned how to do the graph, draw the picture. (Wink) - Mar 23rd 2009, 06:46 AMADARSH
A simple answer to your question is

-Roots are not real as square root of negative is not real

-Meaning graph never touches x axis , or in other words the quadratic function never has zero value

-This means that the quadratic is either always positive or always negative

(since to change from +ve to -ve you need to cross 0 )

**Result:**

Value of equation for all x is either always positive or always negative

----------------------------

**Application**:

Put x = any number , lets take it as 2

$\displaystyle 2^2+2\times 2+7 = 15 $

15>0, as derived earlier for all values of x this is equality holds that

$\displaystyle x^2+2x+7 > 0$

thus answer is every real x

-------------------------------------------

No real need to draw a graph or learning it for answering this - Mar 23rd 2009, 07:07 AMprincess_21
- Mar 23rd 2009, 07:10 AMADARSH
- Mar 23rd 2009, 07:13 AMprincess_21
- Mar 23rd 2009, 07:14 AMprincess_21
Thank you everyone for your help.. I think I need to read more about this..