Question

Скласти Алгоритм Для Розв*язання, квадратного рівняння

Answer 1

См. блок-схему
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Answer 2

Algorithm for Solving a Quadratic Equation

To solve a quadratic equation of the form ax^2 + bx + c = 0, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here's an algorithm to solve a quadratic equation:

1. Start by obtaining the values of a, b, and c from the equation ax^2 + bx + c = 0. 2. Calculate the discriminant, which is the value inside the square root in the quadratic formula: discriminant = b^2 - 4ac. 3. Check the value of the discriminant: - If the discriminant is positive, there are two real solutions. - If the discriminant is zero, there is one real solution. - If the discriminant is negative, there are no real solutions. 4. Calculate the solutions using the quadratic formula: - If the discriminant is positive, calculate both solutions using the formula: x1 = (-b + √discriminant) / (2a) and x2 = (-b - √discriminant) / (2a). - If the discriminant is zero, calculate the solution using the formula: x = -b / (2a). - If the discriminant is negative, there are no real solutions.

Note: The algorithm assumes that the equation is in standard form (ax^2 + bx + c = 0) and that the coefficients a, b, and c are real numbers.

Let's consider an example to illustrate the algorithm:

Example: Solve the quadratic equation 2x^2 + 5x - 3 = 0.

1. From the equation, we have a = 2, b = 5, and c = -3. 2. Calculate the discriminant: discriminant = 5^2 - 4 * 2 * (-3) = 49. 3. Since the discriminant is positive, there are two real solutions. 4. Calculate the solutions using the quadratic formula: - x1 = (-5 + √49) / (2 * 2) = (-5 + 7) / 4 = 2 / 4 = 0.5 - x2 = (-5 - √49) / (2 * 2) = (-5 - 7) / 4 = -12 / 4 = -3

Therefore, the solutions to the quadratic equation 2x^2 + 5x - 3 = 0 are x = 0.5 and x = -3.

Please note that the algorithm can be implemented in various programming languages, and the specific syntax may vary.