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  4. If x3-2 x2-9 x+18=0 and A=|1 2 3 4 x 6 7 8 9| then the maximum value of A is

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Q. If $x^{3}-2 x^{2}-9 x+18=0$ and $A=\begin{vmatrix}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{vmatrix}$ then the maximum value of $A$ is

KCETKCET 2021Determinants

Solution:

$(x-2)\left(x^{2}-9\right)=0$
$x=2,3,-3$
$f(x)=|A|=-12 x+60$
Max value at $x=-3$
$\therefore |A|=96$