gregman999
Answered

One root of f(x)=x^3-9x^2+26x-24 is x = 2. What are all the roots of the function? Use the Remainder Theorem.

(options)-- x = 2, x = 3, or x = 4 x = –2, x = –3, or x = –4 x = 1, x = 2, x = 3, or x = 13 x = –1, x = –2, x = –3, or x = –13

Answer :

kudzordzifrancis

Answer:

[tex]x=3[/tex] or [tex]x=4[/tex]

Step-by-step explanation:

the given function is;

[tex]f(x)=x^3-9x^2+26x-24[/tex]

According to the rational roots theorem, the possible rational roots are;

[tex]\pm1,\pm2\pm3,\pm4,\pm6,\pm8,\pm12,\24[/tex].

According to the Remainder Theorem, if [tex]f(a)=0[/tex], then [tex]x=a[/tex] is a zero of the polynomial.

[tex]f(3)=3^3-9(3)^2+26(3)-24[/tex]

[tex]f(3)=27-81+78-24[/tex]

[tex]f(3)=24-24=0[/tex]

Also,

[tex]f(4)=4^3-9(4)^2+26(4)-24[/tex]

[tex]f(4)=64-144+104-24[/tex]

[tex]f(4)=64-64=0[/tex]

Therefore the other roots are;

[tex]x=3,x=4[/tex]

susplont101

Answer:

A

Step-by-step explanation:

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