Results 1 to 3 of 3

Math Help - Simultaneous Linear and Quadratic Equations

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

    Simultaneous Linear and Quadratic Equations

    Can someone please show me how to work through this type of sum?

    Find the value(s) of a such that the line with equation y=x is tangent to the parabola with equation y=x^2+ax+1

    I know the determinant should equal zero to create a tangent with the parabola, but I don't know how to solve it.

    Any help will be much appreciated,

    Thanks,

    22upon7
    Last edited by 22upon7; March 22nd 2009 at 11:18 PM.
    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
    Can someone please show me how to work through this type of sum?

    Find the value(s) of a such that the line with equation y=x is tangent to the parabola with equation y=x^2+ax+1

    I know the determinant should equal zero to create a tangent with the parabola, but I don't know how to solve it.

    Any help will be much appreciated,

    Thanks,

    22upon7
    x = x^2 + ax + 1 \Rightarrow x^2 + (a - 1)x + 1 = 0.

    You should know that the discriminant of Ax^2 + Bx + C = 0 is B^2 - 4AC.

    Therefore ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    38
    Quote Originally Posted by 22upon7 View Post
    Can someone please show me how to work through this type of sum?

    Find the value(s) of a such that the line with equation y=x is tangent to the parabola with equation y=x^2+ax+1

    I know the determinant should equal zero to create a tangent with the parabola, but I don't know how to solve it.
    I do not know what 'sum' you are referring to. I also do not know what determinant you are referring to either. Are you referring to the discriminant in the quadratic formula?

    We require the two functions to intersect at one and only one point. Setting the y values equal to each other we get,
    x=x^2 +ax+1 \implies 0 = x^2+(a-1)x+1
    In order for this quadratic equation to yield one solution (intersection point) we require the discriminant (the part inside the radical in the quadratic equation) to be zero.
    (a-1)^2 - 4*1*1 = 0 \implies (a-1)^2 = 4 \implies a = 1 \pm 2 \implies a = 3, -1
    hth
    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 Algebra Forum
    Replies: 3
    Last Post: March 23rd 2009, 12:32 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