Sum and Product of Roots (1 Viewer)

[Iguana]

Can anyone explain to me
when:

(a) the roots are reciprocals of each other
(b) the roots are equal in magnitude but opposite in sign
(c) one root equals zero

Thanking you in Advance - Iguana

 

[gurmies]

Alright, your question is kind of ambiguous, but I do understand what you are getting at.

(1) When roots are reciprocals, and especially when you are dealing with an equation of order 2 (quadratic), the product of the roots:

a x 1/a (where "a" is a root) will always be = 1. This makes more difficult polynomial questions much simpler.

(2) When roots are equal in magnitude, but opposite in sign is a more complicated way of saying, if one root is a, the other is - a. Where does this become an advantage to us? Suppose you take the sum of roots:

a + (-a) will always = 0. [provided of course you are dealing with a quadratic equation]

(3) If one root is equal to zero, and you take the sum of roots:

a + 0 = -b/a. It then becomes quite easy to find the other root.

Once again, i'm not too sure what exactly you were asking about. If you post specific questions, I can show you how to apply this knowledge!

 

[3unitz]

let roots of f(x) = ax^2 + bx + c be A and B

A + B = -b/a

AB = c/a

a) when A = 1/B, c/a = 1
c = a

b) when A = -B, -b/a = 0
b = 0

c) when A = 0, c/a = 0
c = 0