Hey guys, having trouble with this problem :-/

Quote:

Show that the equation has roots that are reciprocals of each other. Under what conditions will a quadratic equation in the form have roots that are reciprocals of each other?

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- Feb 24th 2008, 10:25 AMBajanReciprocal Roots
Hey guys, having trouble with this problem :-/

Quote:

Show that the equation has roots that are reciprocals of each other. Under what conditions will a quadratic equation in the form have roots that are reciprocals of each other?

- Feb 24th 2008, 10:36 AMJhevon
you're missing a sign.

do you mean or ?

for the second part, you can expand the general form of: , and see how relate to each other. that's one way. you could also use the quadratic formula to find the roots, and then equate one to the reciprocal of the other and try to solve. things like that.

or perhaps you can use the nature of roots to solve it. if and are the roots of the equation , then and .

then plug in and see what happens.

just play around with it. tell us your findings - Feb 24th 2008, 10:49 AMCaptainBlack
- Feb 24th 2008, 10:50 AMCaptainBlack
- Feb 24th 2008, 01:24 PMSoroban
Hello,Bajan!

Quote:

Under what conditions will a quadratic equation in the form

have roots that are reciprocals of each other?

An equation with "symmetric" coefficients will have reciprocal roots . . .

. . that is: .

The two roots are: .

. . which can be shown to be reciprocals.