Solve each quadratic equation by factoring and check

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

ax²+bx+c = a(x-x1)(x-x2)
2 ) Δ = 0 : one solution : x1 = x2 = -b/2a

ax²+bx+c = a(x-x1)²
3 ) Δ < 0 : no reals solutions... no 

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.