The equation x3 – 3x + a = 0 will have exactly one real root... | MATH - DIFFERENTIATION OF IMPLICIT FUNCTION, PARAMETRIC AND COMPOSITE FUNCTIONS | SolveeIt | Solveeit

Today, August 19

Question

The equation x³ – 3x + a = 0 will have exactly one real root if

A

(0, 2)

B

(– 2, 2)

C

(–∞, –2) ∪ (2, ∞)

D

(– 2, 0)

Answer

(–∞, –2) ∪ (2, ∞)

Explanation

Solution

f(x) = x³ – 3x + a

f ′(x) = 3x² – 3 = 0, x = ± 1

maxima at x = 1

minima at x = – 1

f(–1) f(1) > 0

(a + 2) (a – 2) > 0

a < – 2, a > 2