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CBSE Class 10 Answered

If f(x) is a polynomial such that f(a)f(b) <0 , then what is the number of zeros lying between a and b?
Asked by aayanshaditya23 | 18 May, 2019, 09:31: AM
answered-by-expert Expert Answer
f left parenthesis a right parenthesis f left parenthesis b right parenthesis less than 0 rightwards double arrow f left parenthesis a right parenthesis less than 0 space a d space f left parenthesis b right parenthesis greater than 0 space space O R space space f left parenthesis a right parenthesis greater than 0 space a n d space f left parenthesis b right parenthesis less than 0 rightwards double arrow f left parenthesis a right parenthesis space a n d space f left parenthesis b right parenthesis space a r e space o f space o p p o t i t e space s i g n s rightwards double arrow T h e r e space e x i s t space a t space l e a s t space o n e space c space a t space w h i c h space f left parenthesis c right parenthesis equals 0 space b e t w e e n space a space a n d space b S i n c e comma space f left parenthesis a right parenthesis space a n d space f left parenthesis b right parenthesis space a r e space o f space o p p s i t e space s i g n s S o comma space t h e r e space c a n space b e space 1 space o r space 3 space o r space 5 space a n d space s o space o n space n u m b e r space o f space r o o t s space o f space f left parenthesis x right parenthesis space b e t w e e n space a space a n d space b H e n c e comma space t h e r e space c a n space b e space o d d space n u m b e r space o f space z e r o s space o f space f left parenthesis x right parenthesis space l y i n g space b e t w e e n space a space a n d space b
Answered by Renu Varma | 18 May, 2019, 10:59: AM

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