Question 1046439

the zeros of a given function f are
{{{x[1]= -1}}},
{{{x[2]=2}}}, and 
 {{{x[3]=5}}}
use zero product theorem to find {{{f(x)}}}

{{{f(x)=(x-x[1])(x-x[2])(x-x[3])}}}

{{{f(x)=(x-(-1))(x-2)(x-5)}}}

{{{f(x)=(x+1)(x-2)(x-5)}}}

{{{f(x)=(x+1)(x-2)(x-5)}}}

{{{f(x)=x^3-6x^2+3x+10}}}

a. What are the zeros of the function {{{g(x)=2f(x)}}}?

use factored form {{{f(x)=(x+1)(x-2)(x-5)}}}

{{{g(x)=2((x+1)(x-2)(x-5))}}}

{{{0 = 2 (x-5) (x-2) (x+1)}}}...basically nothing will change
the zeros of a  function {{{g(x)}}} are same as of a {{{ f(x)}}}

{{{x[1]= -1}}},
{{{x[2]=2}}}, and 
 {{{x[3]=5}}}

b. What are the zeros of the function {{{h(x)=f(2x) }}}

if {{{f(x)=x^3-6x^2+3x+10}}}, then
{{{h(x)=f(2x) =(2x)^3-6 (2x)^2+3 (2x)+10}}}
{{{h(x) =8x^3-24x^2+6x+10}}}

{{{h(x)  = 2(2x+1)(2x-5)(x-1)}}}

 {{{2(2x+1) (2 x-5) (x-1)=0}}}

 if {{{2 (2x+1) =0}}}, then {{{(2x+1) =0}}}-> and {{{x =-1/2}}}

 if {{{(2 x-5) =0{{{-> then {{{2x=5}}}-> and {{{x=5/2}}}
if {{{(x-1)=0}}}-> {{{x=1}}}