FIND INTEGRAL ROOTS OF :
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FIND INTEGRAL ROOTS OF :

How to integrate when there is a radical in the denominator
How to integrate when there is a radical in the denominator

CBSE Class 9 Answered

FIND INTEGRAL ROOTS OF :x cubed plus x squared plus x minus 3

x cubed plus x squared plus x minus 3

Asked by harshmandlik | 04 Aug, 2014, 05:42: PM

x cubed plus x squared plus x minus 3 equals 0 B y space s u b s t i t u t i o n space m e t h o d comma space w e space c a n space o b s e r v e space t h a t space o n e space r o o t space i s space 1 1 cubed plus 1 squared plus 1 minus 3 equals 0 space left parenthesis T r u e right parenthesis N o w space l e t space t h e space o t h e r space t w o space r o o t s space b e space alpha space a n d space beta w e space h a v e comma S u m space o f space t h e space r o o t s equals 1 plus alpha plus beta equals minus 1 P r o d u c t space o f space t w o space r o o t s equals alpha plus beta plus alpha beta equals 1 P r o d u c t space o f space t h r e e space r o o t s equals alpha beta equals 3 C o n s i d e r space alpha plus beta equals minus 2 space a n d space alpha beta equals 3 rightwards double arrow alpha plus 3 over alpha equals minus 2 rightwards double arrow alpha squared plus 3 plus 2 alpha equals 0 therefore alpha equals fraction numerator minus 2 plus-or-minus square root of 4 minus 12 end root over denominator 2 end fraction rightwards double arrow O t h e r space t w o space r o o t s space a r e space n o t space r e a l space r o o t s S o space i n t e g r a l space r o o t s space o f space x cubed plus x squared plus x minus 3 equals 0 space i s space o n l y space 1

Answered by Dharma Teja | 05 Aug, 2014, 08:24: AM

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