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CBSE Class 11-science Answered

f(x)=x^2-2ax+a^2-1 and g(x)=(4b-b^2-5)x^2-(2b-1) +3b and a,b belong to R. 1)The values of a for which f(x)=0 are greater  than -2 but lesser than 4 lie in the interval? 2)If roots of the equation g(x)=0 lie on either side of unity tehn number of integarl values of b=? 3)If f(x)<0 for all x belongs to (0,1) the a lies in the interval?  
Asked by aahnik.mohanty | 20 Jun, 2019, 10:25: PM
answered-by-expert Expert Answer
3 right parenthesis f left parenthesis x right parenthesis equals x squared minus 2 a x plus a squared minus 1 f left parenthesis x right parenthesis less than 0 x squared minus 2 a x plus a squared minus 1 less than 0 open parentheses x minus a close parentheses squared less than 1 rightwards double arrow 0 less than open parentheses x minus a close parentheses squared less than 1 rightwards double arrow 0 less than open parentheses x minus a close parentheses less than 1 N o w comma space 0 less than x less than 1 rightwards double arrow x less than 1 space a n d space x minus a less than 1 rightwards double arrow negative x greater than negative 1 space a n d space minus x plus a greater than negative 1 rightwards double arrow a greater than negative 2 A l s o comma space x greater than 0 space a n d space x minus a greater than 0 rightwards double arrow negative a greater than 0 rightwards double arrow a less than 0 rightwards double arrow negative 2 less than a less than 0 H e n c e comma space a element of left parenthesis negative 2 comma 0 right parenthesis
 
Note:- Only one question will be answered in one query. Please ask in separate queries for more answers. 
Answered by Renu Varma | 25 Jun, 2019, 10:30: AM

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