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  • For what value of a in the interval [ 7pi /6 , 7pi /4] does the quadratic expression x^2cot a +2xsquare root (tan a) +tan a assume only positive values.

For what value of a in the interval [ 7pi /6 , 7pi /4] does the quadratic expression x^2cot a +2xsquare root (tan a) +tan a assume only positive values.

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Solution:   Given ,    f(x)=x^2 cot a+2xsqrt an a+ an a

            ain[frac7pi6,frac7pi4]  For   f(x)> 0,forall x in R,D< 0

      \ \ Rightarrow 4 an a< 4Rightarrow an a< 1\ \ Rightarrow ain [frac7pi6,frac5pi4]cup [frac3pi2,frac7pi4]hspace0.5cm......(1)

and      cot a> 0Rightarrow frac7pi6leq aleq frac3pi2hspace0.5cm......(2)

Intersection  of (1) and (2) is ain [frac7pi6,frac5pi4)
        

Posted by

Deependra Verma

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