Question 938659
If one root of a polynomial (quadratic, cubic or whatever) equation is 3,
the equation is {{{(x-3)*something=0}}} or an equivalent equation.
For example, the equations
{{{(x-3)*1=0}}} , 
{{{(x-3)*(x+2)=0}}} ,
{{{(x-3)*(x+2)*7=0}}} ,
{{{(x-3)*(x+2)*(x+1)=0}}} , and
{{{(x-3)*(x^2+x+1)=0}}} all have an {{{x=3}}} solution/root.
 
If one root of a quadratic equation is 5/3 then equation is
{{{(x-5/3)*(x-root)=0}}} or equivalent.
What is the other {{{root}}} ?
If the other root is 3, the equation could be
{{{(x-5/3)*(x-3)=0}}} , which can be written in a more familiar form by multiplying the indicated product:
{{{(x-5/3)*(x-3)=0}}}--->{{{x^2-3x-(5/3)x+(5/3)*3=0}}}--->{{{x^2-(14/3)x+5=0}}} .
Multiplying both sides of the equal sign times 3, it looks even nicer:
{{{x^2-(14/3)x+5=0}}}--->{{{3*(x^2-(14/3)x+5)=3*0}}}--->{{{3x^2-3*(14/3)x+3*5=0}}}--->{{{3x^2-14x+15=0}}} .