How do you write a polynomial with roots – square root of 3 , square root of 3 , and 2 ?

1 Answer
mason m
Jan 14, 2016

#y=x^3-2x^2-3x+6#

Explanation:

Note that if a polynomial has root #b#, then the binomial #(x-b)# is a factor of the polynomial.

Thus, since the roots are #-sqrt3,sqrt3,2#, the polynomial can be expressed as

#y=(x-(-sqrt3))(x-sqrt3)(x-2)#
#=(x+sqrt3)(x-sqrt3)(x-2)#
#=(x^2-3)(x-2)#
#=x^3-2x^2-3x+6#

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