if alpha and beta are the zeroes of the polynomial f(x)=x square-k(x+1)-c.Then prove that (alpha+1)(beta+1)=1-c

Asked by mkvinvestments6 | 14th Sep, 2015, 06:05: PM

Expert Answer:

Hi

begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus k left parenthesis x plus 1 right parenthesis minus c equals x squared minus k x minus k minus c alpha space a n d space beta space a r e space t h y e space z e r o e s space o f space f left parenthesis x right parenthesis S u m space o f space r o o t s equals alpha plus beta equals fraction numerator negative left parenthesis negative k right parenthesis over denominator 1 end fraction equals k P r o d u c t space o f space r o o t s equals alpha beta equals fraction numerator negative k minus c over denominator 1 end fraction minus k minus c L. H. S. equals left parenthesis alpha plus 1 right parenthesis left parenthesis beta plus 1 right parenthesis equals alpha beta plus alpha plus beta plus 1 equals negative k minus c plus k plus 1 equals negative c plus 1 equals 1 minus c equals R. H. S. end style

Answered by  | 14th Sep, 2015, 06:23: PM

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