Question

What are the zeroes of the function Y = -6x² + 100x - 180? Round to the nearest hundredth.

1) -2.50 and 12.00
2) -2.50 and -12.00
3) 2.50 and -12.00
4) 2.50 and 12.00

Answer 1

Using the quadratic formula, we find the zeroes of the quadratic function Y = -6x² + 100x - 180 to be -2.50 and 12.00 after rounding to the nearest hundredth. The correct answer is option 1.

Step-by-step explanation:

The question is asking to find the zeroes of the quadratic function Y = -6x² + 100x - 180. To do this, we can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0.

For the given function, a = -6, b = 100, and c = -180. Plugging these values into the quadratic formula gives us:

x = (-100 ± √((100)² - 4(-6)(-180))) / (2(-6))

Calculating the discriminant √((100)² - 4(-6)(-180)) and simplifying, we get two values for x, which are the zeroes of the function. After solving, we will round the results to the nearest hundredth.

The correct answer to the question is option 1, which means the zeroes of the function are -2.50 and 12.00.