Results 1 to 2 of 2

Math Help - finding common roots

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    4

    finding common roots

    please help me with this question

    for which real values of b do the equations

    x^3 + bx^2 + 2bx -1 =0 and x^2 + (b-1)x + b = 0

    have a common root

    thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,245
    Thanks
    1
    Let x_0 be the common root.
    \displaystyle\left\{\begin{array}{cc}x_0^3+bx_0^2+  2bx_0-1=0 & (1)\\<br />
x_0^2+(b-1)x_0+b=0 & (2)\end{array}\right.
    We observe that x_0\neq 0.
    Multiplying (2) by x_0 and then substracting from (1), we have
    x_0^2+bx_0-1=0\Rightarrow x_0^2+bx_0=1 (3)
    The equality (2) can be written as x_0^2+bx_0-x_0+b=0
    Using (3) we have 1-x_0+b=0\Rightarrow x_0=b+1.
    Plug x_0 in (2) and we have 2b^2+3b=0\Rightarrow b_1=0, \ b_2=\displaystyle-\frac{3}{2}.
    If b=0, the common root is x_0=1.
    If \displaystyle b=-\frac{3}{2}, the common root is \displaystyle x_0=-\frac{1}{2}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Quadratic and cubic equation -show that -(common roots)
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: August 19th 2011, 11:47 PM
  2. Finding common plane
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 31st 2010, 02:14 AM
  3. Equations with Common Roots
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: August 25th 2009, 03:12 AM
  4. Finding common ratio and more?
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: January 4th 2009, 04:23 PM
  5. Finding a point in common
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 19th 2007, 04:42 AM

Search Tags


/mathhelpforum @mathhelpforum