Please help with the question,

• carlosego: The correct answer is x^2-2x+2=0
  
   The explanation is shown below:
  
   1. To solve the problem shown in the figure above, you must apply the following proccedure:
  
   2. You have that the roots of the quadratic equation shown in the figure attached in the problem are:
  
    x=-1±i
  
   3.  Then, you know the quadratic formula to solve quadratic equations, which is:
  
   (-b±√(b^2-4ac))/2a
  
   4. You can see in the figure that a=1 and c=2; then, by analizing this, you can conclude that the coefficient b is:
  
   b=-2
  
   5. Therefore, you can conclude tha the quadratic equation is:
  
   x^2-2x+2=0
  
   6. If you want to verify it, apply the quadratic formula to the quadratic equation shown above and you will obtain the roots shown in the figure.
• aencabo:

  To form a quadratic equation, let α and β be the two roots.

  Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).

  According to the problem, roots of this equation are α and β.

  Therefore,

  α + β = - baba and αβ = caca.

  Now, ax22 + bx + c = 0

  ⇒ x22 + babax + caca = 0 (Since, a ≠ 0)

  ⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]
  

  ⇒ x22 - (sum of the roots)x + product of the roots = 0

  ⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)

  Formula (i) is used for the formation of a quadratic equation when its roots are given.

  Given the roots: (-1+-i)

  where; i=sqrt(-1)

  Thus, the answer is (2x)

  You can also do checking to verify if x^2+2x+2 will have roots equal to (-1+-i)