Number of integers satisfying the inequality, x 4 - 29 x 2 + 100 ≤ 0 is

Step-by-step solution

We have, x 4 - 29 x 2 + 100 ≤ 0 . ⇒ x 4 - 25 x 2 - 4 x 2 + 100 ≤ 0 ⇒ x 2 - 4 x 2 - 25 ≤ 0 ⇒ 4 ≤ x 2 ≤ 25 or x - 2 x + 2 x - 5 x + 5 ≤ 0 By wavy curve method and using sign scheme for this inequality, ⇒ x ∈ - 5 , - 2 ∪ 2 , 5 Integers satisfying above are ± 5 ,   ± 4 ,   ± 3 ,   ± 2 . So, there are eight integers.