helping solving sum and product of roots

Question

 

1.what is the sum of the roots of the equation ax^2 + bx + c = 0

 

  what is the product of its roots

 

 

 

2.  solve the equation x^3 + 2x^2 + x + 2= 0, if -2 is a root

 

 

3.  given the equation x^3 - 2x^2 + x - 3 + 0, what are the possible rational roots.  Please  help solve.

 

 

A big thanks

Answer 1

1.what is the sum of the roots of the equation ax^2 + bx + c = 0

what is the product of its roots.

 

The roots are x1,x2= (-b±√(b²-4*a*c))/2*a

 

adding the roots x1+x2=-b/a multiplying the roots x1*x2=c/a (this one takes a couple of steps to derive)

 

2.If -2 is a root then x+2 is a factor dividing the cubic by x+2 gives x²+1 as the other factor so the other two roots are ±i

 

3. It's not an equation???

Jim