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

One solution

Step-by-step explanation:

Plug this equation in standard form to the quadratic formula.

That is -b plus or minus the square root of b squared -4ac and the whole thing divided by 2a.

Quadratic equations in standard form are written as ax squared plus bx plus c.

Your a for this equation is 9.

B is 12

C is 4.

Here is a simple rule to identify if an equation has one solution, two solutions, or no solution.

Your b squared minus 4ac is called your discriminant value.

if b squared minus 4ac is greater than 0, then there are two real-number solutions. Meaning there are two x-intercepts.

If b squared minus 4ac is equal to 0, then there is only one real solution.

Meaning there is only one x-intercepts.

if b squared minus -4ac is less than 0, then there are no real solution. Meaning there are no x-intercepts.

In this case, there discriminant value for this equation is 0, meaning this equation had one real-number solution.

Hope this helps!