Final answer:
The quadratic equation 9z²+12z+4=0 is solved using the quadratic formula to find that the solution is z = -2/3, which is a double root since the discriminant is zero.
Step-by-step explanation:
To solve the quadratic equation 9z²+12z+4=0 using the quadratic formula, we first identify the coefficients a, b, and c. In this equation, a=9, b=12, and c=4. The quadratic formula is given by z = (-b ± √(b²-4ac)) / (2a). Applying these values to the quadratic formula, we have:
z = (-(12) ± √((12)²-4(9)(4))) / (2(9))
z = (-12 ± √(144-144)) / 18
z = (-12 ± √(0)) / 18
z = (-12 ± 0) / 18
z = -12 / 18
z = -2 / 3
Since the discriminant (b²-4ac) is 0, there is one real double root for the equation. Therefore, the solution is z = -2/3.