In what conditions will a quadratic equation in the form ax²+bx c=0have roots that r reciprocals of each other

Question

i am in grade 11 and i got this for home work: under what conditions will a quadratic equation in the form ax² + bx c = 0 have roots that are reciprocals of each other? please help me

Answer 1

You could easily have a parabola with reciprocal roots, such as the one pictured here:

http://s236.photobucket.com/albums/ff177/jsardi56/?action=view¤t=reciprocalroots10-1-07.jpg

More generally, start with reciprocal roots, and work backward:
x = n; x = 1/n
x - n = 0; x - 1/n = 0
(x - n)(x - 1/n) = 0
x^2 - nx - 1/nx + n/n = 0
x^2 - ((n^2 +1)/n)x + 1 = 0 ;n ≠ 0
So a quadratic equation that can be put in this form would have reciprocal roots.