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JEE Main20248 Apr 2024Evening ShiftMathematicsLimitsActual

If = _ x 0⁺ ( e ^ x - e ^ x x - x ) and = _ x 0 (1+ x)^ 1 2 x are the roots of the quadratic equation a x^2+b x- e =0 , then 12 _ e ( a + b ) is equal to__________

Correct answer

0

Step-by-step solution

aligned & = _ x 0⁺ e^ x (e^ x - x -1 ) x - x & =1 & = _ x 0 (1+ x)^ 1 2 x & =e^ 1 / 2 & x^2-(1+ e )+ e =0 & a x^2+b x- e =0 & On comparing & a=-1, b= e +1 & 12 (a+b)=12 1 2 =6 aligned

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