Question

Write the polynomial p(x) = x² + 4x + 1 as the product of two first degree polynomials. Find the solution of the equation p (x) = 0.

Answer 1

x² + 4x + 1 = (x – a) (x – b) = x² – (a + b) x + ab(1)

a + b = –4, ab = 1, a – b = 2√3 

a = –2 + √3, b = –2 – √3 (1)

x² + 4x + 1 =(x + 2+ √3 ) (x + 2 – √3 ) (1) 

x² + 4x + 1 = 0 =>(x + 2 + √3 )(x + 2 –√3 ) = 0 (1)

x = –2 – √3 ,or x = –2 + √3