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Answer:
The zeros are 0, 4, 6.
The y-intercept is 0.
Step-by-step explanation:
f(x) = x^3 - 10x^2 + 24x
x^3 - 10x^2 + 24x = 0
x(x^2 - 10x + 24) = 0
x(x - 4)(x - 6) = 0
x = 0 or x - 4 = 0 or x - 6 = 0
x = 0 or x = 4 or x = 6
y-intercept:
Since x = 0 is a root, that means that the point (0, 0) is part of the function. That makes the y-intercept 0.
You can also solve for the y-intercept by letting x = 0 in the function and solving for f(0).
Let x = 0.
f(0) = 0^3 - 10(0^2) + 24(0)
f(0) = 0
y-intercept: 0