He polynomial of degree 5, p (x) p (x) has leading coefficient 1, has roots of multiplicity 2 at x = 4 x=4 and x = 0 x=0, and a root of multiplicity 1 at x = - 4 x=-4 find a possible formula for p (x) p (x).

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Mathematics

Cristopher Delacruz

11 February, 05:06

He polynomial of degree 5, p (x) p (x) has leading coefficient 1, has roots of multiplicity 2 at x = 4 x=4 and x = 0 x=0, and a root of multiplicity 1 at x = - 4 x=-4 find a possible formula for p (x) p (x).

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Ladybug · Answer 1

Root of x = 4 means (x - 4) is a factorMultiplicity of two means that (x - 4) is used twice root of x = - 4 means that (x + 4) is a factormultiplicity of 1 means it is used once so y = a (x-4) (x-4) (x + 4) y = a (x^3 - 4x2 - 16x + 64)

Thus, any polynomial with these zeroans d as a minimum these multiplicities will be a multiple (scalar or polynomial) of this P (x).