Question

5. How many real-number solutions does the equation have?

`9x^{2}+12x+4=0`

A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions

explain answer

Answer 1

To find the number of real-number solutions for the equation 9x^2 + 12x + 4 = 0, we can use the discriminant formula:

If the quadratic equation is in the form ax^2 + bx + c = 0, then the discriminant is b^2 - 4ac.

For the equation 9x^2 + 12x + 4 = 0, a = 9, b = 12, and c = 4.

The discriminant is calculated as: b^2 - 4ac = 12^2 - 4*9*4 = 144 - 144 = 0.

If the discriminant is equal to 0, then the equation will have one real solution. Therefore, the answer is:

A. one solution