Final answer:
The quadratic equation 5z²-9z+4=0 is solved using the quadratic formula. The solutions for z are determined to be z = 1 and z = 0.8 after substituting the coefficients into the formula.
Step-by-step explanation:
To solve the quadratic equation 5z²-9z+4=0 using the quadratic formula, we must first identify the coefficients of the equation which are in the form az² + bz + c = 0. Here, a = 5, b = -9, and c = 4.
The quadratic formula is given by:
z = (-b ± √(b² - 4ac)) / (2a)
Substitute the values of a, b, and c into the formula to find the solutions for z:
z = (-(-9) ± √((-9)² - 4(5)(4))) / (2(5))
z = (9 ± √(81 - 80)) / 10
z = (9 ± √(1)) / 10
z = (9 ± 1) / 10
Therefore, the two solutions for z are:
- z = (9 + 1) / 10 = 1
- z = (9 - 1) / 10 = 0.8