Final answer:
The given quadratic equation 10z²-11z+3=0 is solved using the quadratic formula to find two solutions, z = 0.6 and z = 0.5.
Step-by-step explanation:
To solve the equation 10z²-11z+3=0, we can use the quadratic formula, which is applicable for equations of the form az² + bz + c = 0. The quadratic formula states that the solutions for z are given by:
z = −b ± √(b² - 4ac) / (2a)
In our case, a = 10, b = −11, and c = 3. Plugging these values into the quadratic formula gives us:
z = −(−11) ± √((−11)² - 4 × 10 × 3) / (2 × 10)
z = 11 ± √(121 - 120) / 20
z = 11 ± √1 / 20
z = 11 ± 1 / 20
So the solutions are:
- z = (11 + 1) / 20 = 12 / 20 = 0.6
- z = (11 - 1) / 20 = 10 / 20 = 0.5
Hence, the solutions to the quadratic equation are z = 0.6 and z = 0.5.