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  • The values of p , for which both the roots of equation 4x^2-20px+25p^2+15p-66=0 are less than 2 , belong to

The values of p , for which both the roots of equation 4x^2-20px+25p^2+15p-66=0 are less than 2 , belong to

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Solution:   Since both the roots are less than 2 , we have 

           \ \ Rightarrow hspace1cm Dgeq 0Rightarrow 15p-66leq0Rightarrow pleqfrac225\ \ Rightarrow hspace1cm4f(2)> 0Rightarrow 4(25p^2-25p-50)> 0Rightarrow p^2-p-2> 0\ \ Rightarrow hspace1cm-frac202cdot4< 2Rightarrow p< frac43

Taking the intersection of the above three solution , we get    pin(infty,-1).

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Deependra Verma

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