Answer:
f(x) = x^2 - 4x - √5
Explanation:
A polynomial function of least degree with rational coefficients, a leading coefficient of 1, and zeroes at 4 and -√5 can be written as:
f(x) = (x - 4)(x + √5)
This is a polynomial of degree 2 (a quadratic), and it has rational coefficients as it is made up of two binomials, both of which have integers as their coefficients. The leading coefficient is 1, and the zeroes are at 4 and -√5.
In standard form, f(x) = ax^2 + bx + c, we can write it as
f(x) = x^2 - 4x - √5
Note that the above polynomial uses irrational numbers, which are not rational coefficients, but it has zeroes at the given value of 4 and -√5.