How do you find all real zeros of the function #f(x)=2x(x-9)^2(x-2)^2#?

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Alan P. Share
Jan 10, 2017

Answer:

Real zeros at #x in {0,9,2}#

Explanation:

As an explicit expansion can be factored as:
#f(x)=color(red)(""(2x))xxcolor(blue)(""(x-9))xxcolor(green)(""(x-9))xxcolor(orange)(""(x-2))xxcolor(magenta)(""(x-2))#

Each factor gives one (not necessarily unique) zero:
#{: ("factor:",color(red)(""(2x)),color(blue)(""(x-9)),color(green)(""(x-9)),color(orange)(""(x-2)),color(magenta)(""(x-2))), ("implied zero:",color(white)("X")color(red)0,color(white)("X")color(blue)9,color(white)("X")color(green)9,color(white)("X")color(orange)2,color(white)("X")color(magenta)2) :}#

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