Option D: [tex]f(x) = (x - 7)(x - 5)(x - 5)(x + 2)[/tex] is the polynomial
Explanation:
Given that we need to determine the polynomial that has a leading coefficient of 1, roots -2 and 7 with multiplicity 1 and root 5 with multiplicity 2
Option A: [tex]f(x) = 2(x + 7)(x + 5)(x - 2)[/tex]
The polynomial has roots -7, -5 and 2 with multiplicity 1.
Hence, Option A is not the correct answer.
Option B: [tex]f(x) = 2(x - 7)(x - 5)(x + 2)[/tex]
The polynomial has roots 7,5 and -2 with multiplicity 1.
Hence, Option B is not the correct answer.
Option C: [tex]f(x) = (x + 7)(x + 5)(x + 5)(x - 2)[/tex]
The polynomial has roots 2 and -7 with multiplicity 1 and root -5 with multiplicity 2.
Hence, Option C is not the correct answer.
Option D: [tex]f(x) = (x - 7)(x - 5)(x - 5)(x + 2)[/tex]
The polynomial has roots -2 and 7 with multiplicity 1 and root 5 with multiplicity 2.
Hence, Option D is the correct answer.
