Question

For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?

Answer 1

Calculation:

⇒ (n - 5) (n - 10) - 3 × (n - 2) ≤ 0

⇒ n2 - 15n + 50 - 3n + 6 ≤ 0

⇒ n2 - 18n + 56 ≤ 0

⇒ (n - 14) (n - 4) ≤ 0

⇒ 4 ≤ n ≤ 14, n = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

⇒ Total integer is 11

∴ The required result will be 11.