If alpha and betaare the zeros of the quadratic polynomial f(x)=x2-p(x+1)-c , show that (alpha+1)(beta+1)=1-c

Asked by yadnya patil | 2nd Jun, 2014, 10:46: AM

Expert Answer:

C o n s i d e r 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 comma space x squared minus p open parentheses x plus 1 close parentheses minus c equals 0 rightwards double arrow space x squared minus p x minus open parentheses p plus c close parentheses equals 0 L e t space 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 q u a d r a t i c space p o l y n o m i a l. T h e n space S u m space o f space t h e space z e r o e s space i s space alpha plus beta equals minus open parentheses minus p close parentheses T h e space p r o d u c t space o f space t h e space z e r o e s space i s space alpha beta equals open square brackets minus open parentheses p plus c close parentheses close square brackets W e space n e e d space t o space s h o w space t h a t space open parentheses alpha plus 1 close parentheses open parentheses beta plus 1 close parentheses equals 1 minus c N o w space c o n s i d e r space t h e space l e f t space h a n d space s i d e space o f space t h e space e x p r e s s i o n : space open parentheses alpha plus 1 close parentheses open parentheses beta plus 1 close parentheses equals alpha beta plus alpha plus beta plus 1 space space space space space space space space space space space space space space space space space space space space space space equals open square brackets minus open parentheses p plus c close parentheses close square brackets plus p plus 1 space space space space space space space space space space space space space space space space space space space space space space equals minus p minus c plus p plus 1 space space space space space space space space space space space space space space space space space space space space space space equals 1 minus c space space space space space space space space space space space space space space space space space space space space space space equals R. H. S H e n c e space p r o v e d.

Answered by Vimala Ramamurthy | 2nd Jun, 2014, 11:35: AM