Results 1 to 4 of 4

Math Help - Simultaneous Linear and Quadratic Equations

  1. #1
    Junior Member 22upon7's Avatar
    Joined
    Nov 2008
    Posts
    60

    Simultaneous Linear and Quadratic Equations

    Now I know the rules about this one, But I can't work out the second half of the sum,

    1st half:
    1. Find the value of c such that the line with equation y=2x+c is a tangent to the parabola with equation y=x^2+3x

    2x+c = x^2+3x
    x^2+x-c=0

    the determinant = 0 then there is only one intersection (tangent)

    through DOPS

    x^2+x+\frac{1}{4}=0
    (x-\frac{1}{2})^2=0

    therefore c = \frac{-1}{4}

    Now this is the part, I don't understand,

    2. Find the possible values of c such that the line with equation
    y=2x+c twice intersects the parabola with equation y=x^2+3x

    Any help would be much appreciated,

    Thanks,

    22upon7
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by 22upon7 View Post
    Now I know the rules about this one, But I can't work out the second half of the sum,

    1st half:
    1. Find the value of c such that the line with equation y=2x+c is a tangent to the parabola with equation y=x^2+3x

    2x+c = x^2+3x
    x^2+x-c=0

    the determinant = 0 then there is only one intersection (tangent)

    through DOPS

    x^2+x+\frac{1}{4}=0
    (x-\frac{1}{2})^2=0

    therefore c = \frac{-1}{4}

    Now this is the part, I don't understand,

    2. Find the possible values of c such that the line with equation y=2x+c twice intersects the parabola with equation y=x^2+3x

    Any help would be much appreciated,

    Thanks,

    22upon7
    You require the discriminant to be greater than zero.
    Last edited by mr fantastic; March 23rd 2009 at 01:01 AM. Reason: Discriminant, not determinant ... The power of suggestion on the tired mind
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member 22upon7's Avatar
    Joined
    Nov 2008
    Posts
    60
    Thanks, so would that be proved like this:

    1-4c=0

    1=4c

    \frac{1}{4}=c

    Therefore c>-\frac{1}{4}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by 22upon7 View Post
    Thanks, so would that be proved like this:

    1-4c=0

    1=4c

    \frac{1}{4}=c

    Therefore c>-\frac{1}{4}
    The discriminant of x^2 + x - c is not 1 - 4c.

    Once you calculate correct discriminant you need to solve the following inequality for c:

    discriminant > 0.
    Last edited by mr fantastic; March 23rd 2009 at 01:02 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simultaneous quadratic equations
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 14th 2011, 05:30 PM
  2. Simultaneous quadratic equations
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 24th 2010, 05:15 AM
  3. Simultaneous Linear and Quadratic Equations
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 23rd 2009, 01:10 AM
  4. Replies: 3
    Last Post: February 27th 2009, 07:05 PM
  5. Replies: 3
    Last Post: March 30th 2008, 01:30 AM

Search Tags


/mathhelpforum @mathhelpforum