Question

Range of 'a' for which x³ – 12x + [a] = 0 has exactly one real root is (–∞, p) ∪ [q, ∞), then ||p| – |q|| is ______.

विकल्प

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Range of 'a' for which x³ – 12x + [a] = 0 has exactly one real root is (–∞, p) ∪ [q, ∞), then ||p| – |q|| is 1.00.

Explanation:

Let f(x) = x³ – 12x + [a]

f'(x) = 3x² – 12 = 0

⇒ x = ±2

f(2).f(–2) > 0

⇒ ([a] – 16)([a] + 16) > 0

⇒ [a] < –16 and [a] > 16

⇒ a < –16 ∪ a > 17

⇒ a ∈ (–∞, –16) ∪ [17, ∞)

⇒ p = –16, q = 17

⇒ |p| – |q| = – 1

⇒ ||p| – |q|| = 1