Question

If the equation x² + 2(k + 2)x + 9k = 0 has equal roots then k = ?

Options

• 1 or 4

• –1 or 4

• 1 or –4

• –1 or –4

Answer 1

1 or 4

Explanation: 

It is given that the roots of the equation (x² + 2(k + 2)x + 9k = 0) are equal.

∴ (b² – 4ac) = 0 

⇒ {2(k + 2)}² – 4 × 1 × 9k = 0 

⇒ 4(k² + 4k + 4) – 36k = 0 

⇒ 4k² + 16k + 16 – 36k = 0  

⇒ 4k² – 20 + 16 = 0 

⇒ k² – 5k + 4 = 0 

⇒ k² – 4k – k + 4 = 0 

⇒ k(k – 4) – (k – 4) = 0 

⇒ (k – 4) (k – 1) = 0 

⇒ k = 4 or k = 1