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CBSE Class 10 Answered

if alpha and beta are the zeros of polynomial x square - 2 X + 5 then find the quadratic polynomial whose zeros are alpha+beta and one upon alpha + one upon beta
Asked by vinitgandhi114 | 31 Oct, 2019, 13:26: PM
answered-by-expert Expert Answer
alpha space a n d space beta space a r e space t h e space z e r o e s space o f space t h e space p o l y n o m i a l space P left parenthesis x right parenthesis equals x squared minus 2 x plus 5 rightwards double arrow alpha plus beta equals 2 space a n d space alpha beta equals 5 space.... space left parenthesis i right parenthesis T o space f i n d space t h e space q u a d r a t i c space p o l y n o m i a l space w h o s e space z e r o e s space a r e space alpha plus beta space a n d space 1 over alpha plus 1 over beta C o n s i d e r comma space s u m space o f space t h e space z e r o e s equals open parentheses alpha plus beta close parentheses plus open parentheses 1 over alpha plus 1 over beta close parentheses equals open parentheses alpha plus beta close parentheses plus open parentheses fraction numerator alpha plus beta over denominator alpha beta end fraction close parentheses equals 2 plus 2 over 5 equals 12 over 5 P r o d u c t space o f space t h e space z e r o e s space equals space open parentheses alpha plus beta close parentheses open parentheses 1 over alpha plus 1 over beta close parentheses equals open parentheses alpha plus beta close parentheses open parentheses fraction numerator alpha plus beta over denominator alpha beta end fraction close parentheses equals 2 cross times 2 over 5 equals 4 over 5 H e n c e comma space t h e space r e q u i r e d space q u a d r a t i c space p o l y n o m i a l space i s space Q left parenthesis x right parenthesis equals x squared minus 12 over 5 x plus 4 over 5
Answered by Yasmeen Khan | 31 Oct, 2019, 17:25: PM

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