Number of integers satisfying the inequality,& x^ 4 - 29x^ 2 + 100...

We have,& $x^{4} - 29x^{2} + 100 \le 0$.

$⇒ x^{4} - 25x^{2} - 4x^{2} + 100 \le 0$

$⇒ \left(x^{2} - 4\right)\left(x^{2} - 25\right) \le 0$

$⇒ 4 \le x^{2} \le 25$

or~\left(x - 2\right)\left(x + 2\right)\left(x - 5\right)\left(x + 5\right) \le 0$</p><p>By wavy curve method and using sign scheme for this inequality,</p><p>$⇒ x \in \left[-5, - 2\right] \cup \left[2, 5\right]

Integers satisfying above are $\pm5, \pm4, \pm3, \pm2.</p><p>So, there are eight integers.</p></blockquote>$