Final answer:
The quadratic polynomial with a sum of zeros as 5 and a product of zeros as 0 is x² - 5x.
Step-by-step explanation:
A quadratic polynomial having a sum of zeros as 5 and product of zeros as 0 can be expressed using the relationship between the coefficients and the zeros of the polynomial. For a quadratic polynomial of the form ax² + bx + c = 0, the sum of the zeros (-b/a) must equal 5, and the product of the zeros (c/a) must equal 0. Given these conditions, it is clear that c, the constant term, must be 0, for the product of the zeros to be 0. As for the sum of the zeros being 5, the coefficient b needs to be -5 when a is chosen to be 1 (to avoid fractions and to simplify), as the coefficient a is a nonzero constant term in a quadratic equation. So, we get a = 1, b = -5, and c = 0. Hence, the quadratic polynomial that satisfies these conditions is x² - 5x.