Results 1 to 9 of 9

Math Help - find the values of m so that the equation will have two equal roots.

  1. #1
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    find the values of m so that the equation will have two equal roots.

    is m the slope? what formula i may use to solve for this?
    Attached Thumbnails Attached Thumbnails find the values of m so that the equation  will have two equal roots.-m.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: find the values of m so that the equation will have two equal roots.

    Just because the textbook says y = mx + b does not mean you should automatically assume m is the slope. Besides, what slopes are mentioned in this problem?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: find the values of m so that the equation will have two equal roots.

    no, im solving it this way that i have to divide both sides of the equation by x^2+ 1 then m = 1 - 4 sq. root of 3 x underneath x^2+1 sir may i know the next move for the value of m?

    thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: find the values of m so that the equation will have two equal roots.

    Okay, so m = \frac{1 - 4 \sqrt{3}x}{x^2 + 1}. But does get you any closer to a solution?

    I would start with the original equation and expand the LHS, yielding

    mx^2 + m = 1 - 4 \sqrt{3} x

    mx^2 + 4 \sqrt{3} x + (m-1) = 0

    This has two equal roots if and only if the discriminant is zero.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: find the values of m so that the equation will have two equal roots.

    sir im solving for the discriminant.... that a = m, b = 4, and c = (m-1) is this correct? the equate to zero.

    D = 4^2 - 4(m)(m-1)
    D = 16 - 4m^2 + 4m
    0 = 16 - 4m^2 + 4m
    0 = -4(m^2-m-4)
    0 = m^2-m-4 sir this not a factorable expression... what is the next sir?

    thanks
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: find the values of m so that the equation will have two equal roots.

    There should be a 4 \sqrt{3} in there, i.e.


    D = (4 \sqrt{3})^2 - 4m(m-1) = 0

    48 - 4m^2 + 4m = 0

    m^2 - m - 12 = 0, this factors. If it didn't factor, how would you solve it then?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: find the values of m so that the equation will have two equal roots.

    if i were to solve it sir , i will use quadratic formula. is it ok?


    factor like ( m - 4) (m + 3) = 0

    then m = 4 or m = - 3

    is that right sir?
    Last edited by rcs; July 30th 2012 at 10:55 PM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,391
    Thanks
    757

    Re: find the values of m so that the equation will have two equal roots.

    in that case, check your answer:

    m = 4:

    4(x2 + 1) = 1 - (4√3)x

    4x2 + 4 = 1 - (4√3)x

    4x2 + (4√3)x + 3 = 0

    since we are supposed to have 2 equal roots, this should factor as:

    (2x + √3)2 = 0. does it?

    m = -3:

    -3(x2 + 1) = 1 - (4√3)x

    -3x2 - 3 = 1 - (4√3)x

    3x2 + (4√3)x + 4 = 0

    again, this "ought" to factor as:

    (√3x + 2)2 = 0. does it?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: find the values of m so that the equation will have two equal roots.

    thanks Deveno
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. values of x of factored equation (roots)
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 30th 2012, 09:15 PM
  2. find set of values, district roots
    Posted in the Algebra Forum
    Replies: 10
    Last Post: January 12th 2012, 01:42 PM
  3. Find the value of equation with equal roots
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: November 17th 2010, 02:03 AM
  4. find out the equation with the roots given
    Posted in the Algebra Forum
    Replies: 6
    Last Post: September 28th 2009, 07:45 AM
  5. Solving Quadratic Equation With Equal Roots
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 27th 2009, 12:32 AM

Search Tags


/mathhelpforum @mathhelpforum