Final answer:
To find the non-negative zero of the function f(x) = 6x² - 9x - 6, apply the quadratic formula to yield two solutions, x = 2 and x = -0.5. The non-negative zero of the function is x = 2.
Step-by-step explanation:
The student is asking to find the non-negative zero of the quadratic function f(x) = 6x² - 9x - 6. To find the zeros of a quadratic function, one can use the quadratic formula, which is derived from the general form ax² + bx + c = 0. The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). In our case,
a = 6,
b = -9, and
c = -6. Applying the coefficients to the quadratic formula gives us the potential zeros of the function.
Plugging these values into the quadratic formula we get:
x = (9 ± √((-9)² - 4 · 6 · (-6))) / (2 · 6)
Calculating under the radical gives:
x = (9 ± √(81 + 144)) / 12
x = (9 ± √225) / 12
x = (9 ± 15) / 12, which gives us two solutions:
x = 24/12 or
x = -6/12.
Hence, the solutions are x = 2 and
x = -0.5.
Since the student asked for the non-negative zero, the answer is x = 2.