Question

4x^2+12x+4 factorise

Answer 1

4x² + 12x + 4 = 0
x² + 3x + 1 = 0
x² + 3x = -1
x² + 3x + (3/2)² = (3/2)² -1
(x + 3/2)² = 9/4 - 1 = 5/4
take square root both sides,
(x + 3/2) = ±√5/2
x = -3/2 ± √5/2

{x + 3/2 +√5/2} and {x + 3/2 - √5/2} are factors of 4x² + 12x + 4