CBSE Class 12-science Answered

If m∈Z and the equation mx2+(2m−1)x+(m−2)=0mx2+(2m-1)x+(m-2)=0 has rational roots, then m is of the form

Asked by mohit16071997 | 06 Jan, 2020, 01:22: PM

Expert Answer

We need to find the value of m such that the equation mx²+(2m-1)x+(m-2)=0 has rational roots where m is an integer.

I n space t h e space g i v e n space q u a d r a t i c space e q u a t i o n comma space a equals m comma space b equals 2 m minus 1 space a n d space c equals m minus 2 D i s c r i m i n a n t space i s space D equals b squared minus 4 a c equals open parentheses 2 m minus 1 close parentheses squared minus 4 open parentheses m close parentheses open parentheses m minus 2 close parentheses equals 4 m squared minus 4 m plus 1 minus 4 m squared plus 8 m equals 4 m plus 1 T h e space r o o t s space a r e space r a t i o n a l space w h e n space t h e space d i s c r i m i n a n t space i s space a space p e r f e c t space s q u a r e rightwards double arrow 4 m plus 1 equals n squared space comma space n element of straight integer numbers rightwards double arrow m equals fraction numerator n squared minus 1 over denominator 4 end fraction equals fraction numerator open parentheses n minus 1 close parentheses open parentheses n plus 1 close parentheses over denominator 4 end fraction N o w comma space n space s h o u l d space b e space a n space o d d space i n t e g e r rightwards double arrow n equals 2 k plus 1 comma space f o r space k element of straight integer numbers space rightwards double arrow m equals fraction numerator open parentheses 2 k plus 1 minus 1 close parentheses open parentheses 2 k plus 1 plus 1 close parentheses over denominator 4 end fraction rightwards double arrow m equals fraction numerator open parentheses 2 k close parentheses open parentheses 2 k plus 2 close parentheses over denominator 4 end fraction equals fraction numerator 4 k open parentheses k plus 1 close parentheses over denominator 4 end fraction rightwards double arrow m equals k open parentheses k plus 1 close parentheses comma space k element of straight integer numbers

Answered by Renu Varma | 07 Jan, 2020, 11:42: AM

CBSE Class 12-science Answered

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CBSE Class 12-science Answered

Application Videos

ProblemsbasedonIntoFunction-I

ProblemsbasedonIntoFunction-II

Concept Videos

Properties of Inverse Trigonometry Part - 1

Graphical representation of inverse trigonometric funct ...

Continuous and Discontinuous function

Relationship between continuity and differentiability - ...

Introduction to Relations

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