First slide

Introduction to sets

Question

Number of integers satisfying the inequality, $x^{4} - 29 x^{2} + 100 \leq 0$ is

Moderate

A

2
B

4
C

6
D

8

Solution

We have $x^{4} - 29 x^{2} + 100 \leq 0$
$\begin{array}{ll} \Rightarrow (x^{2} - 4) (x^{2} - 25) \leq 0 \\ \Rightarrow 4 \leq x^{2} \leq 25 \\ \Rightarrow x \in [- 5, - 2] \cup [2, 5] \end{array}$
Integers satisfying above are $\pm 5, \pm 4, \pm 3, \pm 2$
So, there are eight integers.

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