Question

The polynomial x³ – kx² + 9x has three real zeros if and only if, k satisfies. 

(a) |k| ≤ 6 

(b) k = 0 

(c) |k| > 6 

(d) |k| ≥ 6

Answer 1

(d) |k| ≥ 6

x³ – kx² + 9x = 0 

⇒ x (x² – kx + 9) = 0 

x = 0 is one real root. If the remaining roots to be real if the

b² – 4ac ≥ 0 

⇒ k² – 36 ≥ 0 

⇒ k² ≥ 36 

⇒ |k| ≥ 6