Final answer:
A polynomial function with rational real coefficients, a leading coefficient of 3, and roots of square root of 5 and 2 can be represented as f(x) = 3(x - 2)(x - √5).
Step-by-step explanation:
A polynomial function with rational real coefficients, a leading coefficient of 3, and roots of square root of 5 and 2 can be represented as:
f(x) = 3(x - 2)(x - √5)
To find the polynomial function, we use the fact that the roots of a polynomial are the values of x for which the polynomial is equal to zero. Since the leading coefficient is 3, we multiply the expression (x - 2)(x - √5) by 3 to obtain the polynomial function.
In this case, the polynomial function of lowest degree is a quadratic function.