Results 1 to 2 of 2

Math Help - Find all values of parameter 'a' if?

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Find all values of parameter 'a' if?

    For what values of 'a' does the equation ax^2 - (a + 1)x + 3 = 0, have roots lying between 1 and 2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Last_Singularity's Avatar
    Joined
    Dec 2008
    Posts
    157
    The quadratic formula states for a quadratic equation ax^2 + bx + c = 0, the solution is
    x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    In your case, a = a, b = -(a+1), c = 3, so your solutions are
    x = \frac{a+1 \pm \sqrt{(a+1)^2 - 4(a)(3)}}{2a} = \frac{a+1 \pm \sqrt{a^2 - 10a + 1}}{2a}

    The small root is
    x_1 = \frac{a+1 - \sqrt{a^2 - 10a + 1}}{2a}
    while the larger root is
    x_2 = \frac{a+1 + \sqrt{a^2 - 10a + 1}}{2a}

    Your constraint say that 1<x_1 and x_2<2, so find the values of a such that those two inequalities are satisfied.

    Can you take it from there?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find loci (parameter involved)
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 17th 2011, 04:35 AM
  2. Find a value for parameter...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 28th 2010, 03:37 AM
  3. eliminating parameter to find cartesian eq.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 29th 2010, 03:08 AM
  4. removing parameter t to find the locus
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 13th 2010, 11:40 PM
  5. Replies: 1
    Last Post: May 24th 2009, 06:16 AM

Search Tags


/mathhelpforum @mathhelpforum