please help me please with this one question

Question

Identify the number and type of solutions for the equation 9x² − 12x + 4 = 0.

A.) 1 nonreal complex

B.) 1 real

C.) 2 nonreal complex

D.) 2 real

Please give and only give the explanation and the solution.

Answer 1

To solve this problem you have to use the discriminant formula (The discriminant is the part under the square root in the quadratic formula applied to y = ax²+bx+c

b²-4ac = 0 1 real solution

b²-4ac > 0 2 real solution

b²-4ac

9x² − 12x + 4 = 0.

a= 9

b= -12

c = 4

b²- 4a*c

(-12)² -4(9)(4)

144 - 144 = 0

Therefore 1 real solution

ANS: B.) 1 real