Question

A function P(x) has both 2 and 3 as roots, x=5 is a solution such that P(5)=0, and the degree of P(x) is 2. Explain why no such polynomial exists.

Answer 1

Explanation:

Roots mean the the function has a result of zero at that point. This function would therefore have zeros at 2, 3 and 5 and the degree would be at LEAST 3 and possibly higher depending on the multiplicity of each root.

factors would be

(x - 2)ⁿ¹(x - 3)ⁿ²(x - 5)ⁿ³ where n₁, n₂ and n₃ are Whole numbers ≥ 1