Question
Fri April 17, 2015 By: Jerlin George

If α and β are the zeroes of the polynomial x2 + 4x + 3, then form a polynomial whose zeroes are 1+ β/α and 1+α/β.

Expert Reply
satyajit samal
Fri April 17, 2015
I f space alpha space a n d space beta space a r e space r o o t s space o f space t h e space e q u a t i o n space x squared plus 4 x plus 3 equals 0 comma space t h e n space alpha plus beta equals negative 4 alpha beta equals 3. L e t space P space a n d space Q space a r e space t h e space r o o t s space o f space t h e space e q u a t i o n space w h o s e space r o o t s space a r e space 1 plus beta over alpha space a n d space 1 plus alpha over beta H e n c e comma space P plus Q equals 2 plus beta over alpha plus alpha over beta equals 2 plus fraction numerator beta squared plus alpha squared over denominator alpha beta end fraction equals 2 plus fraction numerator open parentheses alpha plus beta close parentheses squared minus 2 alpha beta over denominator alpha beta end fraction equals 2 plus fraction numerator 16 minus 6 over denominator 3 end fraction equals 2 plus 10 over 3 equals 16 over 3 P Q equals open parentheses space 1 plus beta over alpha close parentheses open parentheses 1 plus alpha over beta close parentheses equals 2 plus beta over alpha plus alpha over beta equals 16 over 3 H e n c e comma space t h e space p o l y m o n i a l space i s x squared minus open parentheses P plus Q close parentheses x plus P Q equals x squared minus 16 over 3 x plus 16 over 3
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