The image shows a multiple-choice question in Russian related to mathematics. The question asks to select the correct statement. The options provided are mathematical expressions for roots (x1 and x2) of a quadratic equation, with some options already evaluated. The input field at the top shows '-1;1,3:0'. Below this, the text 'Выберите верное утверж' means 'Choose the correct statement'. The options are: 1. x1 = (2 - sqrt(16))/2 = -1, x2 = ? 2. x1 = (1 - sqrt(16))/2 = 1, x2 = ? 3. x1 = 0, x2 = (2 + sqrt(16))/2 = ? 4. x1 = (2 - sqrt(16))/2 = -1, x2 = ? I need to determine which of these options, if any, correctly calculates the roots of a quadratic equation given the format. The initial input field '-1;1,3:0' might represent roots, but the options are presented as calculations. Let's evaluate the given expressions. For option 1 and 4: x1 = (2 - sqrt(16))/2 = (2 - 4)/2 = -2/2 = -1. This matches the given x1. We need to find x2 if this were a complete equation. For option 2: x1 = (1 - sqrt(16))/2 = (1 - 4)/2 = -3/2 = -1.5. This does not match the stated x1=1. For option 3: x1 = 0. This is given. x2 = (2 + sqrt(16))/2 = (2 + 4)/2 = 6/2 = 3. This gives x1=0 and x2=3. Let's assume the initial input '-1;1,3:0' is not directly relevant to the options and focus on evaluating the options themselves as potential solutions to an implied quadratic equation. The question asks to choose the *correct statement*. This implies one of the provided calculations for x1 and x2 is correct. The structure of the options suggests that they are presenting possible results for roots. Let's re-examine them. It's possible the question implicitly uses the quadratic formula where D = b^2 - 4ac and x = (-b ± sqrt(D)) / 2a. Let's assume a quadratic equation of the form ax^2 + bx + c = 0. If we consider the first and fourth options, x1 = -1. If the equation was, for example, x^2 + x = 0, then x(x+1) = 0, so x1=0, x2=-1. Or if it was x^2 - 2x - 3 = 0, then (x-3)(x+1)=0, so x1=3, x2=-1. In this case, x1=-1 is a correct root for certain equations. Let's look at option 3: x1 = 0, x2 = (2 + sqrt(16))/2 = (2+4)/2 = 3. This means the roots are 0 and 3. A quadratic equation with these roots would be x(x-3) = 0, which is x^2 - 3x = 0. Here a=1, b=-3, c=0. If we use the quadratic formula: x = (3 ± sqrt((-3)^2 - 4*1*0)) / (2*1) = (3 ± sqrt(9)) / 2 = (3 ± 3) / 2. So x1 = (3-3)/2 = 0, and x2 = (3+3)/2 = 6/2 = 3. This option is a correct calculation for roots if the equation was x^2 - 3x = 0. However, the format of the options presents a calculation that leads to x1 and then states 'x2 = ...'. It seems like option 3 is presenting a potential calculation for x2, and perhaps x1=0 is given as a separate fact. Let's assume the form of the question implies that one of the lines presents a valid pair of roots or a calculation for one root that is correct. Let's consider the possibility that the provided options are evaluations of a quadratic formula. The typical form is x = (-b ± sqrt(b^2 - 4ac)) / 2a. Let's analyze the given options more closely, assuming they are trying to represent the roots of a quadratic equation. Option 1 and 4: $$x_1 = \frac{2 - \sqrt{16}}{2} = \frac{2 - 4}{2} = \frac{-2}{2} = -1$$. This calculation is correct. The option states $$x_1 = -1$$. This is a valid root for some quadratic equations. Option 2: $$x_1 = \frac{1 - \sqrt{16}}{2} = \frac{1 - 4}{2} = \frac{-3}{2} = -1.5$$. The option states $$x_1 = 1$$. This is incorrect based on the calculation. Option 3: $$x_1 = 0, x_2 = \frac{2 + \sqrt{16}}{2} = \frac{2 + 4}{2} = \frac{6}{2} = 3$$. This option presents two roots, $$x_1=0$$ and $$x_2=3$$. This is a valid calculation for $$x_2$$, and $$x_1=0$$ is given. If the quadratic equation was $$x^2 - 3x = 0$$, then the roots are indeed 0 and 3. The question asks to choose the *correct statement*. Since options 1 and 4 are identical and present a correct calculation for $$x_1 = -1$$, and option 3 presents a correct calculation for $$x_2 = 3$$ with a given $$x_1 = 0$$, we need to determine which statement is considered 'correct'. Let's re-evaluate option 3. It states $$x_1 = 0, x_2 = \frac{2 + \sqrt{16}}{2}$$. The calculation for $$x_2$$ is correct, yielding 3. So the roots are 0 and 3. This is a consistent statement. Let's re-evaluate option 1 and 4. They state $$x_1 = \frac{2 - \sqrt{16}}{2} = -1$$. This calculation is correct. However, only $$x_1$$ is calculated. It is very likely that these options are presenting the calculation of one of the roots, and the equality sign indicates the result of that calculation. Given the choices, option 3 seems to be the most complete as it provides both roots and one of them is derived from a calculation. However, the initial input '-1;1,3:0' is puzzling. If we interpret this as roots: -1, 1, 3, 0, it's too many roots for a quadratic. If we interpret it as parameters, it's unclear. Let's assume the question is about finding roots from a quadratic equation. The expression $$\frac{2-\sqrt{16}}{2}$$ is a common way to write one of the roots using the quadratic formula, where the discriminant is 16. For example, if $$b^2 - 4ac = 16$$. If we assume $$a=1$$, then $$b^2 - 4c = 16$$. Let's consider the possibility that the options are intended to be evaluated. Options 1 and 4 both state $$x_1 = \frac{2-\sqrt{16}}{2} = -1$$. This equality is true. Option 3 states $$x_1=0$$ and $$x_2 = \frac{2+\sqrt{16}}{2} = 3$$. This statement is also true if the equation has roots 0 and 3. However, the structure of multiple-choice questions often implies that only one option is entirely correct. Without the original quadratic equation, it's hard to definitively say which set of roots is implied. Let's focus on the calculations presented as equalities. Option 1: $$\frac{2-\sqrt{16}}{2} = -1$$. This is mathematically correct. Option 2: $$\frac{1-\sqrt{16}}{2} = 1$$. This is mathematically incorrect since $$\frac{1-4}{2} = -1.5 eq 1$$. Option 3: $$x_1 = 0, x_2 = \frac{2+\sqrt{16}}{2} = 3$$. The calculation of $$x_2$$ is correct. If $$x_1=0$$ is also given, then this is a statement about roots 0 and 3. Option 4: $$\frac{2-\sqrt{16}}{2} = -1$$. This is mathematically correct. It's identical to option 1. In a typical multiple-choice setting, identical options are unusual unless one is a distractor. However, if both are mathematically correct statements, and the question asks for the correct statement, then both could be valid. But if this is a single-choice question, there might be an intended interpretation. Let's consider the possibility that the initial input '-1;1,3:0' is related. If we assume the question is asking to *select* a correct calculation of roots, and the calculation in option 1/4 is $$x_1 = -1$$, and in option 3, $$x_2 = 3$$. The input field has '-1;1,3:0'. If we ignore the ':' and assume ';' and ',' as separators, we have {-1, 1, 3, 0}. If these are roots, there are 4 of them, which is not for a quadratic. Let's assume the question is well-posed and there is a single correct answer among the options. Options 1 and 4 are identical. This is a strong indicator that one of them is the intended answer. The calculation $$\frac{2-\sqrt{16}}{2} = -1$$ is correct. Let's re-examine option 3. If the roots are 0 and 3, then $$x^2 - 3x = 0$$. The formula for roots is $$x = \frac{-b ± \sqrt{b^2-4ac}}{2a}$$. For $$x^2 - 3x = 0$$, $$a=1, b=-3, c=0$$. So $$x = \frac{3 ± \sqrt{(-3)^2 - 4(1)(0)}}{2(1)} = \frac{3 ± \sqrt{9}}{2} = \frac{3 ± 3}{2}$$. So $$x_1 = \frac{3-3}{2} = 0$$ and $$x_2 = \frac{3+3}{2} = 3$$. The calculation in option 3 is $$x_2 = \frac{2+\sqrt{16}}{2} = 3$$. This suggests that the numerator might be $$-b$$ if $$b$$ was $$-2$$, but then $$\sqrt{D}$$ would need to be $$\sqrt{16}=4$$, and $$2a$$ would be 2. If $$2a=2$$, then $$a=1$$. If $$-b=-2$$, then $$b=2$$. So if $$a=1, b=2$$, then $$b^2 - 4ac = 2^2 - 4(1)c = 4 - 4c = 16$$. So $$-4c = 12$$, $$c=-3$$. The equation would be $$x^2+2x-3=0$$. The roots are $$x = \frac{-2 ± \sqrt{16}}{2} = \frac{-2 ± 4}{2}$$. So $$x_1 = \frac{-2-4}{2} = -3$$, and $$x_2 = \frac{-2+4}{2} = 1$$. This does not match option 3's roots (0 and 3) or the calculation in option 1/4 ($$x_1=-1$$). Let's consider the possibility that the options are presenting correct calculations of *one* of the roots using the quadratic formula, and the question is asking which of these calculations/statements is correct. Statement 1: $$x_1 = \frac{2 - \sqrt{16}}{2} = -1$$. The calculation is correct. The statement is true. Statement 4: $$x_1 = \frac{2 - \sqrt{16}}{2} = -1$$. The calculation is correct. The statement is true. Statement 3: $$x_1 = 0, x_2 = \frac{2 + \sqrt{16}}{2} = 3$$. The calculation of $$x_2$$ is correct. If $$x_1=0$$ is a given condition for this option, then the statement is true for the roots 0 and 3. Since options 1 and 4 are identical, and the calculation is mathematically correct, it is highly probable that this is the intended correct answer. Typically, in such questions, the equality sign indicates a true mathematical statement. Both options 1 and 4 present a true mathematical statement. If we have to pick one, and options 1 and 4 are identical, it's a bit ambiguous. However, the calculation $$\frac{2-\sqrt{16}}{2} = -1$$ is unequivocally correct. Option 3 also contains a correct calculation $$x_2 = 3$$. Given that option 1 and 4 are the same, and the calculation is correct, I will select one of them. The problem asks to