Question

Find the x-intercept(s) of f(x)=3x^4−30x^3+75x^2
Enter intercept(s) as points

Answer 1

(0, 0) and (5, 0)

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).