SOLUTION: Write a quadratic equation having the given numbers as solutions. {{{1-sqrt(21)/3}}},{{{1+sqrt(21)/3}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Write a quadratic equation having the given numbers as solutions. {{{1-sqrt(21)/3}}},{{{1+sqrt(21)/3}}}      Log On


   

Question 745857: Write a quadratic equation having the given numbers as solutions.
1-sqrt%2821%29%2F3,1%2Bsqrt%2821%29%2F3
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write a quadratic equation having the given numbers as solutions.
1-sqrt%2821%29%2F3,1%2Bsqrt%2821%29%2F3
:
x = 1-sqrt%2821%29%2F3
Write is as single fraction
x = %283-sqrt%2821%29%29%2F3
multiply both sides by 3
3x = 3+-+sqrt%2821%29
subtract 3 from both sides, we can combine plus and minus
3x - 3 = +/-sqrt%2821%29
Square both sides
%283x-3%29%5E2 = 21
FOIL (3x-3)(3x-3); subtract 21 from both sides
9x^2 -18x + 9 - 21 = 0
y = 9x^2 - 18x - 12 is the equation