a) x²+15x+54 = 0.
a = 1
b = 15
c = 54
∆ = b²-4ac
∆ = 15²-4•54
∆ = 225-216
∆ = 9.
x1 = -b+√∆/2a
x1 = -15+3/2
x1 = -12/2
x1 = -6.
x2 = -b-√∆/2a
x2 = -15-3/2
x2 = -18/2
x2 = -9.
a(x-x1)(x-x2) = (x+6)(x+9).
b) 6x²+x-2 = 0.
a = 6
b = 1
c = -2
∆ = b²-4ac
∆ = 1-4•(-2)•6
∆ = 1+48
∆ = 49.
x1 = -b+√∆/2a
x1 = -1+7/12
x1 = 6/12
x1 = 1/2.
x2 = -b-√∆/2a
x2 = -1-7/12
x2 = -8/12
x2 = -2/3.
a(x-x1)(x-x2) = 6(x-1/2)(x+2/3) = 6(2x/2-1/2)(3x/3+2/3) = (2x-1)(3x+2).
Succes!
