Question

For what values of k are the roots of the quadratic equation 3x² + 2kx + 27 = 0 real and equal?

Answer 1

Given: 

3x² + 2kx + 27 = 0 

Here,

a = 3, b = 2k and c = 27  

It is given that the roots of the equation are real and equal; therefore, we have: 

D = 0 

⇒ (2k)² – 4 × 3 × 27 = 0 

⇒ 4k² – 324 = 0  

⇒ 4k² = 324 

⇒ k² = 81 

⇒ k = ±9 

∴ k = 9 or k = –9