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  • The value of a for which one root of the equation (a-5)x^2-2ax+(a-4)=0 is smaller than 1 and the other is greater than 2 is

The value of a for which one root of the equation (a-5)x^2-2ax+(a-4)=0 is smaller than 1 and the other is greater than 2 is

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Solution:

           D> 0,> 4a^2-4(a-5)(a-4)> 0\ \ Rightarrow (9a-20)> 0Rightarrow a> frac209Rightarrow ain(frac209,infty) hspace0.5cm......(1)

          \ \ Rightarrow (a-5)f(1)< 0;(a-5)f(2)< 0\ \ Rightarrow (a-5)(a-5-2a+a-4)< 0\ \ Rightarrow a> 5Rightarrow ain (5,infty)hspace0.5cm.....(2)

     and    (a-5)[(a-5)cdot 4-4a+a-4]< 0\ \ Rightarrow (a-5)(a-24)< 0Rightarrow 5< a< 24\ \ Rightarrow ain(5,24)hspace0.5cm.......(3)

   Using  (1) ,(2) and (3)

The common condition is ain (5,24).

Posted by

Deependra Verma

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