CBSE Class 9 Answered

The polynomials x3+2x2-5ax-8 and x3+ax2-12x-6 when divided by (x-2) and (x-3) leave remainders p and q respectively.If q-p=10;what is the value of ? Sir all these numbers immediately after x are powers of x.

Asked by Harshit Saini | 10 Jul, 2015, 09:06: PM

Expert Answer

L e t space f open parentheses x close parentheses equals x cubed plus 2 x squared minus 5 a x minus 8 space a n d space g open parentheses x close parentheses equals x cubed plus a x squared minus 12 x minus 6 G i v e n space t h a t space p space a n d space q space a r e space t h e space r e m a i n d e r s space w h e n space f open parentheses x close parentheses space a n d space g open parentheses x close parentheses space a r e space d i v i d e d space b y space open parentheses x minus 2 close parentheses space a n d space open parentheses x minus 3 close parentheses space r e s p e c t i v e l y. H e n c e space b y space r e m a i n d e r space t h e o r e m comma space w e space h a v e comma p equals f open parentheses 2 close parentheses equals 2 cubed plus 2 cross times 2 squared minus 5 a cross times 2 minus 8 a n d q equals g open parentheses 3 close parentheses equals 3 cubed plus a cross times 3 squared minus 12 cross times 3 minus 6 rightwards double arrow p equals 8 plus 8 minus 10 a minus 8.. left parenthesis 1 right parenthesis a n d q equals 27 plus 9 a minus 36 minus 6 rightwards double arrow p equals 8 minus 10 a a n d q equals 9 a minus 15.. left parenthesis 2 right parenthesis A l s o space g i v e n space t h a t space q minus p equals 10... left parenthesis 3 right parenthesis H e n c e space f r o m space e q u a t i o n s space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space h a v e comma 9 a minus 15 minus open parentheses 8 minus 10 a close parentheses equals 10 rightwards double arrow 9 a minus 15 minus 8 plus 10 a equals 10 rightwards double arrow 19 a equals 33 rightwards double arrow a equals 33 over 19

Answered by Vimala Ramamurthy | 11 Jul, 2015, 01:15: PM

CBSE Class 9 Answered

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CBSE Class 9 Answered

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