Results 1 to 3 of 3

Math Help - roots of the equation

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    72

    Post roots of the equation

    I have been doing good so far with these problems but I have hit a road block and just can't seem to get pass it. The problems is as follows:
    equation is 2x^2-4x+5=0 and the roots are a and b. I am suppose to finde the value of 1/(a+1) + 1/(b+1). I have already fond that a+b= -b/a = -(-4/2)= 2 and ab=c/a=5/2. Is there anyone out there who can help me?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,629
    Thanks
    430
    Quote Originally Posted by scrible View Post
    I have been doing good so far with these problems but I have hit a road block and just can't seem to get pass it. The problems is as follows:
    equation is 2x^2-4x+5=0 and the roots are a and b. I am suppose to finde the value of 1/(a+1) + 1/(b+1). I have already fond that a+b= -b/a = -(-4/2)= 2 and ab=c/a=5/2. Is there anyone out there who can help me?
    \frac{1}{a+1} + \frac{1}{b+1}

    \frac{(b+1) + (a+1)}{(a+1)(b+1)}

    \frac{a+b+2}{ab + a + b + 1}

    finish now?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    2x^2 - 4x + 5 = 0, dividing BOTH SIDES by 2, we have x^2 - 2x + 5/2 = 0

    a + b = 2 and ab = 5/2

    Or as suggested by SKEETER: evaluate this . . . .

    = [(a + b) + 2]/[(ab) + (a + b) + 1] = [2 + 2]/[5/2 + 2 + 1] = 4/[5/2 + 3] = 4/[11/2] = 8/11.

    Or THIS,

    x^2 - 2x + 5/2 = 0, let x = y - 1, so that the root will be x + 1

    (y - 1)^2 - 2(y - 1) + 5/2 = 0,

    y^2 - 2y + 1 - 2y + 2 + 5/2 = 0,

    y^2 - 4y + 3 + 5/2 = 0

    y^2 - 4y + 11/2 = 0.

    let y = 1/z, so that the root will be 1/(x + 1),

    (1/z)^2 - 4(1/z) + (11/2) = 0, multiply both sides by (2/11)z^2,

    2/11 - (8/11)z + z^2 = 0, re-arranging,

    z^2 - (8/11)z + 2/11 = 0,

    notice that the sum of roots is 8/11.

    -
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Roots of equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 15th 2012, 06:01 PM
  2. Replies: 3
    Last Post: April 6th 2010, 12:36 AM
  3. Roots of equation?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: December 16th 2009, 06:54 PM
  4. Roots of an equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 22nd 2009, 07:31 AM
  5. roots of equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 21st 2007, 06:16 AM

Search Tags


/mathhelpforum @mathhelpforum