Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Quadratic Equation

  1. Apr 10, 2008 #1
    1. The problem statement, all variables and given/known data

    If one root of a quadratic equation with rational co-efficient is (2^(1/2)+1) , then find the quadratic equation.

    2. Relevant equations

    x=(-b+d^1/2)/2a
    d=b^2-4ac


    3. The attempt at a solution

    Well, I cant quite understand this question. Please help me to understand what is given in the following statemnt.
     
  2. jcsd
  3. Apr 10, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    If the only square root in the solution is [itex]\sqrt{2}[/itex], what must d be? Since the only difference between roots of a quadratic equation is that [itex]\pm[/itex] before the square root, what must the other root be?

    Another, more "sophisticated" method:
    Any quadratic, [itex]ax^2+ bx+ c[/itex] can be written [itex]a(x- x_0)(x- x_1)= ax^2- a(x_0+x_1)+ ax_0x_1[/itex] where [itex]x_0[/itex] and [itex]x_1[/itex] are roots of the equation. If one root is [itex]1+ \sqrt{2}[/itex] what must the other be so that both [itex]x_0+ x_1[/itex] and [itex]x_0x_1[/itex] are rational?
     
    Last edited by a moderator: Apr 10, 2008
  4. Apr 10, 2008 #3
    Well, Please check this. I think the othr root is 1-(2^1/2). thre fore the quadratic equation is x^2-2x-1=0
    Am I right?
     
  5. Apr 10, 2008 #4

    HallsofIvy

    User Avatar
    Science Advisor

    Yes, that is correct.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook