The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x=-4. Its lead coefficient is 3. Find a formula for P(x)?

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Anonymous Profile
Anonymous answered
2.369221
Vin Ginge Profile
Vin Ginge answered
The factored formula for the polynomial is, (x - 3)(x - 3)x(x + 4) = 0, given that it has two equal roots when x = 3, a further root when x = 0 and another when x = -4.
This expands to x4 - 2x3 - 15x2 + 36x = 0
As the lead coefficient is 3 then multiply all terms by 3.
3x4 - 6x3 - 45x2 +108x = 0
Then P(x) = 3x4 - 6x3 - 45x2 +108x  [or P(x) = 3x(x3 - 2x2 - 15x + 36)]

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