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Math Help - quadratic equation

  1. #1
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    quadratic equation

    Please help me with this one.

    Show that x^2 + 3x + 5 > 0, for all values of x.

    and

    Show that 2x^2 + 6 > 4x + 1, for all values of x.

    How do i show it,????
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  2. #2
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    Quote Originally Posted by mazy22a View Post
    Please help me with this one.

    Show that x^2 + 3x + 5 > 0, for all values of x.

    and

    Show that 2x^2 + 6 > 4x + 1, for all values of x.

    How do i show it,????
    (1) Try completing the square .
    (2) Rearrange it and try completing the square also .
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  3. #3
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    Quote Originally Posted by mazy22a View Post
    Please help me with this one.

    Show that x^2 + 3x + 5 > 0, for all values of x.

    Mr F says: y = x^2 + 3x + 5 is a positive parabola and has no x-intercepts (I leave the proof of no x-intercepts for you). Therefore ....

    and

    Show that 2x^2 + 6 > 4x + 1, for all values of x.

    Mr F says: 2x^2 + 6 > 4x + 1 => 2x^2 - 4x + 5 > 0. So you need to show that 2x^2 - 4x + 5 > 0. The approach is the same as for the question above.

    How do i show it,????
    ..
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  4. #4
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    cheers

    Quote Originally Posted by mr fantastic View Post
    ..

    So basically i draw a graph.

    And the graph will show that there is no x intercept.

    Okay, cheers.
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  5. #5
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    Quote Originally Posted by mazy22a View Post
    So basically i draw a graph.

    And the graph will show that there is no x intercept.

    Okay, cheers.
    How do you propose to draw the graph? Not the lazy way - using a graphics calculator - I hope.

    To draw the graph by hand (which is what you should be attempting to do) you need to calculate the x-intercepts. Use the quadratic formula to solve x^2 + 3x + 5 = 0. What do you notice about the discriminant ....? Therefore .....
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    How do you propose to draw the graph? Not the lazy way - using a graphics calculator - I hope.

    To draw the graph by hand (which is what you should be attempting to do) you need to calculate the x-intercepts. Use the quadratic formula to solve x^2 + 3x + 5 = 0. What do you notice about the discriminant ....? Therefore .....

    the discirminant is negative, and less than 0.

    D = -11
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