Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Let f(x)=x^2+ x+ where , R and f(f(x))=0 has 2 roots 1 and 2 . Find the value of 2|f(0)| .

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Step-by-step solution

Given, aligned & f(f(1))=0 f(1+ + )=0 & f(f(2))=0 f(4+2 + )=0 aligned Hence, roots of f(x) are + +1 and 2 + +4 Now, sum of roots =3 +2 +5=- 4 +2 =-5 ...(1) Now, product of roots =( + +1)(2 + +4)= ( + +1) 3 2 = ...(2) From Eqns. (1) and (2), b=f(0)= -3 2 Hence, 2|f(0)|=3

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