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CBSE Class 10 Answered

if alpha,beta are the zeroes of xsquare +px +q. then find the polynomial having 1/alpha and 1/beta as its zeroes
Asked by ajayrath7 | 15 Mar, 2019, 08:15: PM
answered-by-expert Expert Answer
given polynomial : x2 + px + q = 0  ....................................(1)
 
if α and β are the roots of polynomial, then we have,  x2 - (α + β)x + ( αβ ) = 0  .................................(2)
 
by comparing (1) and (2),   we have   (α + β) = - p   and    α β = q
 
if 1/α and 1/β are the roots of polynomial, then we have,
 
begin mathsize 12px style x squared space minus space open parentheses 1 over alpha space plus space 1 over beta close parentheses space x space plus space open parentheses 1 over alpha space 1 over beta close parentheses space equals space 0

x squared space space minus space open parentheses fraction numerator alpha space plus space beta over denominator alpha beta end fraction close parentheses space x space plus space open parentheses 1 over alpha space 1 over beta close parentheses space equals space space 0 space space space............. left parenthesis 3 right parenthesis
b y space s u b s t i t u t i n g space f o r space alpha space plus space beta space space space a n d space alpha beta space space comma space space w e space h a v e space space x squared space plus space open parentheses p over q close parentheses space x space plus space open parentheses 1 over q close parentheses space equals space 0 end style
 
hence polynomial  q x2 + p x + 1 = 0 have roots 1/α  and  1/β
Answered by Thiyagarajan K | 15 Mar, 2019, 11:16: PM
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