Which is the cubic polynomial in the standard form with roots 3, -6, and 0?

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Answer 1 · 2016-12-04T15:06:25

#x^3+3x^2-18x=0#

roots are:

#x=0;" "x=3;" "x=-6#

hence the corresponding linear factors are:

#x;" "(x-3);" "(x+6)#

the cubic is them formed by their products

#x(x-3)(x+6)=0#

multiply out.

#x(x^2+3x-18)=0#

#x^3+3x^2-18x=0#

Answer 2 · 2016-12-04T15:07:30

#x^3+3x^2-18x#

The simplest polynomial with zeros #3#, #-6# and #0# is:

#f(x) = (x-3)(x+6)x#

#color(white)(f(x)) = x^3+3x^2-18x#

Any polynomial in #x# with these zeros will be a multiple (scalar or polynomial) of this #f(x)#.