Final answer:
To solve the quadratic equation z²-9z+14=0, use the quadratic formula. The solutions are z=7 and z=2.
Step-by-step explanation:
To solve the quadratic equation z²-9z+14=0, we can use the quadratic formula. First, let's identify the values of a, b, and c. Here, a is equal to 1, b is equal to -9, and c is equal to 14.
Now, plug these values into the quadratic formula: z = (-b ± √(b²-4ac)) / (2a). Substituting the values, we get z = (-(-9) ± √((-9)²-4(1)(14))) / (2(1)). Solving further, we have z = (9 ± √(81-56)) / 2. This simplifies to z = (9 ± √25) / 2. Finally, we get two solutions: z = (9 + 5) / 2 = 7 and z = (9 - 5) / 2 = 2.