Question

In the given polynomial x^2-2x-√5, find the values of
(I) alpha- beta
(II)alpha/beta+beta/alpha
(III)(alpha^2-beta^2)-(alpha-beta)^2-(alpha+beta)^2
where alpha and beta are the zeroes of the polynomial.

Answer 1

hi friend,


given polynomial

x²-2x-√5

let œ,ß be the zeros of the polynomial

we know that œ+ß=-b/a=2

œß=c/a=-√5

(1) œ-ß=??

we know that (œ-ß)²=(œ+ß)²-4œß

→(œ-ß) ²=(2)²-4(-√5)

→(œ-ß) ²=4+4√5

→(œ-ß)=±(2+2√5)

(2).œ/ß+ß/œ

→œ²+ß²/œß

→(œ+ß)²-2œß/œß

→(2)²-2(-√5)/-√5

→4+2√5/-√5

→-(4+2√5)/√5

(3).(œ²-ß²)-(œ-ß)²-(œ+ß)²

→œ²-ß²-œ²-ß²+2œß-œ²-ß²-2œß

→-œ²-3ß²


I hope this will help u :)