Question #02e01

1 Answer
Jim G.
Nov 21, 2017

#y=x^3-x^2-48x+48#

Explanation:

#"given the roots of a polynomial"#

#"say "x=a,x=b,x=c" then"#

#(x-a),(x-b),(x-c)" are the factors of the polynomial"#

#"the polynomial is then the product of the factors"#

#rArrp(x)=a(x-a)(x-b)(x-c)larrcolor(blue)"a is a multiplier"#

#"here the given roots are "x=1" and "x=4sqrt3#

#"to form a cubic (degree 3 polynomial) requires 3 roots"#

#"note that irrational roots usually occur in pairs"#

#x=4sqrt3" is a root then "x=-4sqrt3" is also a root"#

#"the 3 roots are "x=1,x=4sqrt3,x=-4sqrt3#

#rArr(x-1),(x-4sqrt3),(x+4sqrt3)" are factors"#

#rArry=a(x-1)(x-4sqrt3)(x+4sqrt3)larr"let a =1"#

#rArry=(x-1)(x^2-48)#

#rArry=x^3-48x-x^2+48#

#"a possible cubic is "y=x^3-x^2-48x+48#

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