Question

For what values of p are the roots of the equation 4x² + px + 3 = 0 real and equal?

Answer 1

The given equation is 4x² + px + 3 = 0

This is of the form ax² + bx + c = 0, where a = 4, b = p and c = 3 

∴ D = b² – 4ac

= p² – 4 × 4 × 3

= p² – 48 

The given equation will have real and equal roots if D = 0.  

∴ p² – 48 = 0 

⇒ p² = 48 

⇒ `p = +-sqrt(48) = +-4sqrt(3)` 

Hence, `4sqrt(3)` and `-4sqrt(3)` are the required values of p.