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Quadratic Equation

  • Thread starter ritwik06
  • Start date
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1. Homework Statement

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

2. Homework 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.
 

Answers and Replies

HallsofIvy
Science Advisor
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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:
580
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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?
 
HallsofIvy
Science Advisor
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Yes, that is correct.
 

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