Construct a polynomial function, with 5 zeros, with one zero with a multiplicity of 3, and one with a multiplicity of 2

Answer 1

r₁ = the zero with a multiplicity of 3

r₂ = the zero with a multiplicity of 2

p(x) = A(x - r₁)³ (x - r₂)²

where A ≠ 0.

Answer 2

Consider that a polynomial with five zeros (a, b, c, d, e) can be expressed as

0= (x-a)(x-b)(x-c)(x-d)(x-e)

To solve the problem, let a, b, and c be one value (zero would be easy) and let d and e be a second value (1 would be easy). Plugging in and multiplying gives

0 = x^5 -2x^4 + x^3