Answer:
f(x) = (x - 2)(x - 3)(x - 5)
f(x) = x³ - 10x² + 31x - 30
Step-by-step explanation:
We have to write the equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.
That means at x = 2, x = 3 and at x = 5 the function f(x) will become zero.
Therefore, (x - 2), (x - 3) and (x - 5) are the factors of the function f(x).
Ans the cubic function is f(x) = (x - 2)(x - 3)(x - 5) .......... (1) (Answer)
Now, we have to simplify the right hand side of the equation (1).
Hence, f(x) = (x - 2)(x² - 8x + 15)
⇒ f(x) = x³ - 8x² + 15x - 2x² + 16x - 30
⇒ f(x) = x³ - 10x² + 31x - 30
So, this is the requires equation. (Answer)
