Question

Please help with the question,

Answer 1

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)

Answer 2

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.