SOLUTION: Write a quadratic equation with leading coefficient of 1 having as its two roots the numbers obtained by increasing each root of x^2-2x-5 = 0 by the reciprocal of the other.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write a quadratic equation with leading coefficient of 1 having as its two roots the numbers obtained by increasing each root of x^2-2x-5 = 0 by the reciprocal of the other.       Log On


   

Question 927004: Write a quadratic equation with leading coefficient of 1 having as its two roots the numbers obtained by increasing each root of x^2-2x-5 = 0 by the reciprocal of the other.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write a quadratic equation with leading coefficient of 1 having as its two roots, the numbers obtained by increasing each root of x^2-2x-5 = 0 by the reciprocal of the other.
Find roots of x^2 - 2x - 5 = 0 using the "completing the square" method
x^2 - 2x + ___ = 5
Find half of the value of 2 and square it, add to both sides
x^2 - 2x + 1 = 5 + 1
(x-1)^2 = 6
x - 1 = +/- sqrt%286%29
two solutions
x = 1 + sqrt%286%29
x = 1 - sqrt%286%29
"Find two roots, obtained by increasing each root of by the reciprocal of the other."
Using a calc
1+%2B+sqrt%286%29 + 1%2F%281-sqrt%286%29%29 = 2.75959
1+-+sqrt%286%29 + 1%2F%281%2Bsqrt%286%29%29 = -1.15959
FOIL
(x-2.75959)(x+1.15959) = x^2 + 1.15959x - 2.75959x - 3.20000
y = x^2 - 1.6x - 3.2, is the equation