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  4. Number of integral values of ' x ' such that | x 2-3 x -10|+|11 x - x 2-10|=|8 x -20|, is

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Q. Number of integral values of ' $x$ ' such that $\left| x ^2-3 x -10\right|+\left|11 x - x ^2-10\right|=|8 x -20|$, is

Complex Numbers and Quadratic Equations

Solution:

$\left(x^2-3 x-10\right)\left(11 x-x^2-10\right) \geq 0 $
$\therefore\left(x^2-3 x-10\right)\left(x^2-11 x+10\right) \leq 0$
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$\Rightarrow(x-5)(x+2)(x-1)(x-10) \leq 0 $
$x=-2,-1,0,1,5,6,7,8,9,10 $