Answer:
see explanation
Step-by-step explanation:
Given
f(x) = [tex]x^{4}[/tex] + 3x³ - 4x²
To find the zeros equate f(x) to zero, that is
[tex]x^{4}[/tex] + 3x³ - 4x² = 0 ← factor out x² from each term
x²(x² + 3x - 4) = 0 ← factor the quadratic
x²(x + 4)(x - 1) = 0 ← in standard form
Equate each factor to zero and solve for x
x² = 0 ⇒ x = 0 with multiplicity 2
x + 4 = 0 ⇒ x = - 4
x - 1 = 0 ⇒ x = 1
zeros are x = - 4, x = 0, x = 1
