Let f(x)=x^2(x+2)+x+3. Then

JEE Advanced Mathematics question

Let . Then

(A) and for all Correct
(B) and for all
(C) has a root such that , where is the greatest integer less than or equal to Correct
(D) has exactly one root such that , where is the smallest integer greater than or equal to Correct

Answer: (A),(C),(D)

For :

f(-3-k)=(3+-1-k)+(-k)=-(3++k)-k<0,

f(-2+k)=(k-· k+k+1>0 .

So (a) ✔ and (b) ✘. Also and , so has a root (numerically ).

Number of real roots: ; the local

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Question ID VK-108034