Final answer:
The degree 5 polynomial with zeros 4, (7/2), and 0 (having a multiplicity of 3) will have the form p(x) = (x-4)(x-(7/2))x3. This simplifies to the equation p(x) = x5 - 4x4 - 7x3 + 14x2.
Step-by-step explanation:
The polynomial of degree 5 with zeros at 4, (7/2), and 0 (0 having a multiplicity of 3) can be written using the form p(x) = a(x-r)m, where a is a coefficient, r is a zero, and m is the multiplicity of that zero. Given zeros 4, (7/2), and 0 (with multiplicity 3), the polynomial can be written as p(x) = a(x-4)1(x-(7/2))1(x-0)3. The coefficient 'a' can have any value except for 0. If 'a' equals 1, the polynomial is p(x) = (x-4)(x-(7/2))1x3, which simplifies to: p(x) = x5 - 4x4 - 7x3 + 14x2.
Learn more about Degree 5 Polynomial