Question bank/JEE Main/Mathematics

The set of value of if the equation x^3 - 3x^2 + 2 = k
has only 1 real root is equal to $( - \infty,a) \cup (b,\infty)$. Find
value of $\frac{|10ab|}{3}$

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The graph of f(x) = (x^3 -3x^2 + 2) is
[IMAGE] Hence, for 1 real root of given equation will exist when
$K \in ( - \infty, - 2) \cup (2,\infty)$
$\therefore$ a = - 2 b = 0

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx