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Math Help - [SOLVED] help

  1. #1
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    Question [SOLVED] help

    If I can't factor a quadratic equation what will I do??
    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?
    Last edited by princess_21; March 23rd 2009 at 08:00 AM.
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  2. #2
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    Quote Originally Posted by princess_21 View Post
    If I can't factor a quadratic equation what will I do??
    x^2+2x+7 > or = 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?
    since b^2-4ac < 0 , then the quadratic has no real roots ... which tells you something very valuable regarding its graph.
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    Quote Originally Posted by skeeter View Post
    since b^2-4ac < 0 , then the quadratic has no real roots ... which tells you something very valuable regarding its graph.

    then what will be the answer in this question?? thanks I dont know where to start. can you guide on where to start the process? and then I will try doing the rest thanks
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    Quote Originally Posted by skeeter View Post
    since b^2-4ac < 0 , then the quadratic has no real roots ... which tells you something very valuable regarding its graph.
    This means theres no intersection with the x-axis. if you simply need to sketch the graph find the turning point of the quadratic \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
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    Quote Originally Posted by SirNostalgic View Post
    This means theres no intersection with the x-axis. if you simply need to sketch the graph find the turning point of the quadratic \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
    sorry I didn't understand what you said. can you explain further for me? thanks for your time
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    x^2+2x+7

    \frac{d(y)}{d(x)} = 2x+2
    \frac{d(y)}{d(x)} = 0

    2x+2 = 0
    2x = -2
    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
    x^2+2x+7 (x= -1)<br />
    (-1)^2 +2(-1) +7
    = 6

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

    i swear to god my computer pasted what i wrote twice. What in gods name happened there lol
    Last edited by SirNostalgic; March 23rd 2009 at 06:56 AM. Reason: mumbo jumbo comp
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    Quote Originally Posted by princess_21 View Post
    then what will be the answer in this question?? thanks I dont know where to start. can you guide on where to start the process? and then I will try doing the rest thanks
    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?

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    Quote Originally Posted by stapel View Post
    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?

    i still can't understand. as you see I learn from examples and I can't understand from explanations. can you give an example? thanks
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    Talking

    Quote Originally Posted by princess_21 View Post
    i still can't understand. as you see I learn from examples and I can't understand from explanations. can you give an example? thanks
    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.
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    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by princess_21 View Post
    If I can't factor a quadratic equation what will I do??
    x^2+2x+7 > or = 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?
    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


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

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


    x^2+2x+7 > 0

    thus answer is every real x
    -------------------------------------------

    No real need to draw a graph or learning it for answering this
    Last edited by ADARSH; March 23rd 2009 at 08:00 AM.
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    Quote Originally Posted by ADARSH View Post
    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


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

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


    x^2+2x+7 > 0

    thus answer is every real x
    -------------------------------------------

    No real need to draw a graph or learning it for answering this
    so my answer will be all real numbers??
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  12. #12
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by princess_21 View Post
    so my answer will be all real numbers??
    Yes !

    You are very old now ..
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    Quote Originally Posted by ADARSH View Post
    Yes !

    You are very old now ..

    thanks. i need to do better in my exam.. i need to pass after failing in the first one.




    ***atleast you're older
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  14. #14
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    Thank you everyone for your help.. I think I need to read more about this..
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