Consider-a-polynomial-equation-i-0-n-a-i-x-i-0-a-i-Z-Prove-that-if-a-b-c-is-a-root-of-the-above-equation-then-a-b-c-is-also-a-root-a-b-c-Z-c-is-not-a-whole-square-

Question Number 3451 by prakash jain last updated on 13/Dec/15

Consider a polynomial equation

\underset{i = 0}{\sum^{n}} a_{i} x^{i} = 0, a_{i} \in Z

Prove that if a + b \sqrt{c} is a root of the above

equation then a - b \sqrt{c} is also a root .

a, b, c \in Z, c is not a whole square .

Commented by prakash jain last updated on 13/Dec/15

y e s .

Commented by Filup last updated on 13/Dec/15

a h, i see . You said c \neq w h o l e n u m b e r

if c \in Z, c i s i n t e g e r .

you mean \sqrt{c} is not whole ?

Commented by Filup last updated on 13/Dec/15

a, b \in Z

c \in R

Commented by prakash jain last updated on 13/Dec/15

c \in Z, \sqrt{c} is a surd or complex .