Question:
Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.
Solution:
We have,
$\left(x^{2}-2 x+1\right)(x-4)<0$
$\Rightarrow(x-1)^{2}(x-4)<0$
Equating each one to zero, we obtain $\mathrm{x}=1$ and $\mathrm{x}=4$.
Therefore, 1 and 4 are critical points.
Drawing the number lines, we get:
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Therefore, the solution set of the given inequality is $x \in(-\infty, 1) \cup(1,4)$