Question 927924
use formula:

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

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

{{{f(x)=(x-(-3))(x-5)}}}

{{{f(x)=(x+3)(x-5)}}}

{{{f(x)=x^2-5x+3x-15}}}

{{{f(x)=x^2-2x-15}}}


2. 

{{{ x[1]=1/2}}} and {{{ x[2]=-4 }}}

{{{f(x)=(x-(1/2))(x-(-4))}}}

{{{f(x)=(x-(1/2))(x+4)}}}

{{{f(x)=x^2+4x-(1/2)x-(1/2)4}}}

{{{f(x)=x^2+(8/2)x-(1/2)x-2}}}

{{{f(x)=x^2+(7/2)x-2}}}



3. 

{{{x[1]=sqrt(5)}}} and {{{x[2]=-sqrt(5)}}}

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

{{{f(x)=(x-sqrt(5))(x-(-sqrt(5)))}}}

{{{f(x)=(x-sqrt(5))(x+sqrt(5))}}}
 
{{{f(x)=x^2+cross(x*sqrt(5))-cross(x*sqrt(5))-sqrt(5)*sqrt(5)}}}

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



4. 

{{{x[1]=5+3sqrt(2)}}} and {{{x[2]=5-3sqrt(2)}}}

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

{{{f(x)=(x-(5+3sqrt(2)))(x-(5-3sqrt(2)))}}}

{{{f(x)=(x-5-3sqrt(2))(x-5+3sqrt(2))}}}

{{{f(x)=x^2-5x+3x*sqrt(2)-5x-5(-5)-5*3sqrt(2)-3x*sqrt(2)-3sqrt(2)(-5)-3sqrt(2)3sqrt(2)}}}

{{{f(x)=x^2-5x+cross(3x*sqrt(2))-5x+25-cross(15sqrt(2))-cross(3x*sqrt(2))+cross(15sqrt(2))-9(sqrt(2))^2}}}

{{{f(x)=x^2-5x-5x+25-9*2}}}

{{{f(x)=x^2-10x+25-18}}}

{{{f(x)=x^2-10x+7}}}



5. 

{{{x[1]=6+2i}}} and {{{x[1]=6-2i }}}

{{{f(x)=(x - (6 + 2i))(x - (6 - 2i))}}}

{{{f(x)=(x-6-2i)(x-6+2i)}}}

{{{f(x)=x^2-6x+2i*x-6x+36-12i-2i*x+12i-2i(2i) }}}

{{{f(x)=x^2-12x+cross(2i*x)+36-cross(12i)-cross(2i*x)+cross(12i)-4i^2 }}}

{{{f(x)=x^2-12x+36-4(-1) }}}

{{{f(x)=x^2-12x+36+4 }}}

{{{f(x)=x^2-12x+40 }}}