Question

find the zeroes of the quadratic polynomial f(x)=x2 +4x+4, and verify the relationship between the zeroes and its coefficients

Answer 1

f(x) = x2+ 4x+ 4
      = x2 + 2x + 2x +4
      = x(x +2) + 2(x + 2)
     =  (x+2)(x +2)
thus the zeroes are -2 and-2
then let alpha be -2 and beta be -2
a = 1  b= 4  c = 4
alpha + beta = -2 + -2
                     = -4
-b / a = - 4 / 1
.. alpha + beta = - b/a ---------------- 1
alpha * beta = -2 * -2
                    = 4
c / a              = 4 /1
... alpha * beta = c / a ----------------2

thus from 1 and 2 the relationship is verified.