hello :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x1,2 = (-b±√Δ)/2a
factoring :
ax²+bx+c = a(x-x1)(x-x2)
2 ) Δ = 0 : one solution : x1 = x2 = -b/2a
factoring :
ax²+bx+c = a(x-x1)²
3 ) Δ < 0 : no reals solutions... no
factoring