Respuesta :

Answer:

x = 1, x = 2, x = 5

Step-by-step explanation:

Divide f(x) by (x - 2) using Synthetic division

 2 | 1   - 8   17   - 10

      ↓    2   - 12   10

     --------------------------

      1   - 6    5      0 ← remainder

quotient = x² - 6x + 5 = (x - 1)(x - 5)

f(x) =  (x - 1)(x - 2)(x - 5)

To find the zeros let f(x) = 0 , that is

(x - 1)(x - 2)(x - 5) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

x - 5 = 0 ⇒ x = 5

semsee45

Answer:

x = 1, x = 2, x = 5

Step-by-step explanation:

[tex]f(x)=x^3-8x^2+17x-10[/tex]

if [tex]x - 2[/tex] is a factor of [tex]f(x)[/tex], then

[tex]f(x)=(x-2)(x^2+bx+5)[/tex]

Expand brackets:

[tex]\implies f(x)=x^3+bx^2+5x-2x^2-2bx-10[/tex]

Combine like terms:

[tex]\implies f(x)=x^3+(b-2)x^2+(5-2b)x-10[/tex]

Compare coefficients for [tex]x^2[/tex]:

 [tex]b-2=-8[/tex]

[tex]\implies b=-6[/tex]

Therefore,

[tex]f(x)=(x-2)(x^2-6x+5)[/tex]

Factoring [tex](x^2-6x+5)[/tex]:

[tex]\implies f(x)=(x-2)(x-1)(x-5)[/tex]

To find the zeros of [tex]f(x)[/tex], set the function to zero and solve for [tex]x[/tex]:

[tex]\implies f(x)=0\\\\\implies(x-2)(x-1)(x-5)=0\\\\\implies x=2,x=1,x=5[/tex]

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