SOLUTION: Find the quadratic equation with integer coefficients such that the sum of the roots is {{{ 3/2 }}} and the product of the roots is {{{ 1/4 }}} .

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find the quadratic equation with integer coefficients such that the sum of the roots is {{{ 3/2 }}} and the product of the roots is {{{ 1/4 }}} .      Log On


   

Question 289436: Find the quadratic equation with integer coefficients such that the sum of the roots is +3%2F2+ and the product of the roots is +1%2F4+ .
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let the roots be x & y
xy=1/4
x+y=3/2
x=3/2 -y
y(3/2 -y)=1/4
3y/2 - y^2 = 1/4
6y-4y^2=1
4y^2-6y+1=0
y=(3-sqrt(5)), y=(3+sqrt(5)) or vice versa.
y-(3-sqrt(5))* y-(3+sqrt(5))
=y^2-6y+4
.
Ed