The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².
The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;
P(x) = (x-3) (x-3) (x) (x) (x+1)
The expanded form is therefore;
P(x) = x^5 - 5x⁴- 6x³+ 18x².
Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².
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