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

Hi Jackie R.

You can also just factor it

9x² -12x + 4

9x² -12x + 4 = 0

(3x - 2)(3x - 2)

3x - 2 = 0

3x = 2

x = 2/3

This choice B) 1 real

You can also check it

9(2/3)² -12(2/3) + 4= 0

9(4/9) - 8 + 4 =0

4 - 8 + 4 = 0

8 -8 = 0

I hope this helps.

Answer 2

The most straightforward way to do this is to use the quadratic formula, which gives the solutions as 

x1, x2 = (-b + sqrt(b^2 - 4*a*c))/(2*a).

Here, a = 9 (the coefficient of x^2), b = -12 (the coefficient of x), and c = 4 (the constant). Thus, we get

x1, x2 = (12 + sqrt(12^2 - 4*9*4))/(2*9) = (12 + sqrt(144 - 144))/(2*9) = (12 + sqrt(0))/(2*9) = 12/18 = 2/3.

Thus, there's one real solution, and the answer is (B).