Write the simplest polynomial function with the given roots 1, 4, and 3?

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Answer 1 · 2018-05-14T15:08:18

#p(x)=(x-1)(x-4)##(x-3)#

Answer 2 · 2018-05-14T15:11:21

#y = x^3-8x^2+19x-12#

A polynomial with roots, 1, 4, and 3 will have the factored form:

#y = (x-1)(x-4)(x-3)#

Multiply the last two factors:

#y = (x-1)(x^2-7x+12)#

Distribute the first factor over the second:

#y = x(x^2-7x+12)-1(x^2-7x+12)#

Multiply:

#y = x^3-7x^2+12x-x^2+7x-12#

Combine like terms:

#y = x^3-8x^2+19x-12#