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lyudmila [28]
2 years ago
7

Please help with the question,

Mathematics
2 answers:
castortr0y [4]2 years ago
8 0
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.
zvonat [6]2 years ago
8 0

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

Let us assume that the required equation be ax<span>22</span> + bx + c = 0 (a ≠ 0).

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

Therefore,

α + β = - <span><span>ba</span><span>ba</span></span> and αβ = <span><span>ca</span><span>ca</span></span>.

Now, ax<span>22</span> + bx + c = 0

⇒ x<span>22</span> + <span><span>ba</span><span>ba</span></span>x + <span><span>ca</span><span>ca</span></span> = 0 (Since, a ≠ 0)

⇒ x<span>22</span> - (α + β)x + αβ = 0, [Since, α + β = -<span><span>ba</span><span>ba</span></span> and αβ = <span><span>ca</span><span>ca</span></span>]

⇒ x<span>22</span> - (sum of the roots)x + product of the roots = 0

⇒ x<span>22</span> - 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)

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