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  • Find the values of m , for which exactly one root of the equation x^2-2mx+m^2-1=0 lies in the interval (-2,4) is

Find the values of m , for which exactly one root of the equation x^2-2mx+m^2-1=0 lies in the interval (-2,4) is

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Solution:  Given ,x^2-2mx+m^2-1=0

                            (-2m)^2-4cdot1(m^2-1)> 0Rightarrow 4> 0

                           ecause m in R        ..........(1)

                         \ \ Rightarrow f(-2)f(-4)< 0\ \ Rightarrow (4+4m+m^2-1)(16-8m+m^2-1)< 0

                         \ \ Rightarrow (m+3)(m+1)(m-3)(m-5)< 0\ \Rightarrow min(-3,-1)cup (3,5)hspace0.5cm.........(2)

                     Taking intersection  of (1) and (2)

                       \ \ Rightarrow min (-3,-1)cup(3,5)

             

Posted by

Deependra Verma

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