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CBSE Class 10 Answered

Write cubic polynomial whose zeroes are 2+√5/2, 2-√5/2 and 4
Asked by mkmishra101 | 11 Jun, 2016, 03:48: PM
answered-by-expert Expert Answer
begin mathsize 12px style s u m space o f space z e r o e s equals open parentheses 2 plus fraction numerator square root of 5 over denominator 2 end fraction close parentheses plus open parentheses 2 minus fraction numerator square root of 5 over denominator 2 end fraction close parentheses plus 4 equals 8 S u m space t a k i n g space p r o d u c t space o f space t w o space z e r o e s space a t space a space t i m e equals open parentheses 2 plus fraction numerator square root of 5 over denominator 2 end fraction close parentheses open parentheses 2 minus fraction numerator square root of 5 over denominator 2 end fraction close parentheses plus open parentheses 2 plus fraction numerator square root of 5 over denominator 2 end fraction close parentheses 4 plus open parentheses 2 minus fraction numerator square root of 5 over denominator 2 end fraction close parentheses 4 equals open parentheses 4 minus 5 over 4 close parentheses plus 8 plus 2 square root of 5 plus 8 minus 2 square root of 5 equals 20 minus 5 over 4 equals 75 over 4 P r o d u c t space o f space a l l space z e r o e s equals open parentheses 2 plus fraction numerator square root of 5 over denominator 2 end fraction close parentheses open parentheses 2 minus fraction numerator square root of 5 over denominator 2 end fraction close parentheses 4 equals open parentheses 4 minus 5 over 4 close parentheses 4 equals 16 minus 5 equals 11 S o space t h e space c u b i c space p o l y n o m i a l space c a n space b e x cubed minus open parentheses s u m space o f space a l l space z e r o e s close parentheses x squared plus open parentheses s u m space o f space p r o d u c t space o f space t w o space z e r o e s space a t space a space t i m e close parentheses x minus p r o d u c t space o f space a l l space z e r o e s equals x cubed minus 8 x squared plus 75 over 4 x minus 11 end style
Answered by satyajit samal | 13 Jun, 2016, 09:45: AM

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