The zeros of the given polynomial function is 0, 5, 6.
How to find the zeros of a polynomial function
In mathematics, polynomial functions are expressions represented in variables, these variables are raised to the power of non-negative exponents in conjunction with their coefficients.
To find the zeros of the polynomial function p(x) = x⁶ - 11x⁵ + 30x⁴. We need to factorize and equate the polynomial function to zero.
x⁶ - 11x⁵ + 30x⁴ = 0
x⁴(x² - 11x + 30) = 0
We then need to set the factors to zero and solve for the zeros of x
x⁴ = 0 means x = 0
(x² - 11x + 30) = 0
By factorization:
(x - 5) (x - 6) = 0
x = 5, x = 6
Therefore, the zeros of x = 0, 5, 6.