Answer:
(0, 0) and (5, 0)
Step-by-step explanation:
f(x) = 3x⁴−30x³+75x²
(a) Factor the polynomial
3x⁴−30x³+75x² = 3x²(x² -10² + 25)
= 3x²(x - 5)²
(b) Solve the polynomial
3x²(x - 5)² = 0
x² = 0 x - 5 = 0
x = 0 x = 5
The x-intercepts are at (0, 0) and (5, 0).
The Figure below shows the graph of your polynomial with the x-intercepts at (0, 0) and (5, 0).
