Final answer:
To find the zeros of the quadratic function y = 21x² - 46x + 24, you can use the quadratic formula. The zeros are approximately x ≈ 1.3333 and x ≈ 0.8571.
Step-by-step explanation:
To find the zeros of a quadratic function, you need to set the function equal to zero and solve for x. In this case, the function is y = 21x² - 46x + 24. Set y equal to zero:
0 = 21x² - 46x + 24
Next, you can factor the quadratic equation or use the quadratic formula to find the zeros. Let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values from the given quadratic equation, you get:
x = (-(-46) ± √((-46)² - 4(21)(24))) / (2(21))
Simplifying further, you can calculate the values of x:
x = (46 ± √(2116 - 2016)) / 42
x = (46 ± √100) / 42
x = (46 ± 10) / 42
So, the zeros of the quadratic function are:
x = (46 + 10) / 42 = 56 / 42 =
x ≈ 1.3333
x = (46 - 10) / 42 = 36 / 42 =
x ≈ 0.8571
Learn more about Finding zeros of a quadratic function