Question

Теорема Виета - это широко используемая теорема в математике, которая связана с решением квадратных уравнений. Она была открыта Франциском Виета (1540-1603) в XVI веке и была применена и на другие типы уравнений. Теорема Виета гласит, что для любого квадратного уравнения ax²+bx+c=0 сумма решений должна быть равна -(b/a) и произведение решений должно быть равно c/a. Квадратное уравнение x²+px+q=0 имеет решения x = M и x = N. Какое из этих квадратных уравнений будет иметь решения x=M² и x=N²? A) x²-p² x+q²=0 B) x²-(p²-2q)x+q²=0 C) x²+p²x+q²=0 D) x²-(p²+2q)x+q²=0 пж помогите

Answer 1

Ответ:

C) x²+p²x+q²=0

Объяснение:

x=M, x=N цельные числа, тоесть x=M_2,x=N_2 будет  x² ,p² и q² , ведь они тоже цельные числа.

Answer 2

The Vieta's Theorem and Quadratic Equations

The Vieta's theorem is a widely used theorem in mathematics that is associated with solving quadratic equations. It was discovered by François Viète (1540-1603) in the 16th century and has been applied to other types of equations as well.

According to Vieta's theorem, for any quadratic equation of the form ax² + bx + c = 0, the sum of the solutions must be equal to -(b/a), and the product of the solutions must be equal to c/a.

Now, let's consider the quadratic equation x² + px + q = 0, which has solutions x = M and x = N. We need to determine which of the given quadratic equations will have solutions x = M² and x = N².

To find the answer, we can use the fact that the sum and product of the solutions of a quadratic equation are related to the coefficients of the equation.

Let's analyze each option:

A) x² - p²x + q² = 0 B) x² - (p²-2q)x + q² = 0 C) x² + p²x + q² = 0 D) x² - (p²+2q)x + q² = 0

To determine the sum and product of the solutions for each equation, we can compare the coefficients of the quadratic terms (x²), the linear terms (x), and the constant terms.

For option A: - The sum of the solutions is M² + N². - The product of the solutions is (M²)(N²) = (MN)².

For option B: - The sum of the solutions is (p²-2q) = M² + N². - The product of the solutions is q² = (MN)².

For option C: - The sum of the solutions is -p² = M² + N². - The product of the solutions is q² = (MN)².

For option D: - The sum of the solutions is -(p²+2q) = M² + N². - The product of the solutions is q² = (MN)².

Based on Vieta's theorem, the sum of the solutions should be equal to -(b/a) and the product of the solutions should be equal to c/a.

Comparing the sums and products obtained for each option with the expected values, we can conclude that option C) x² + p²x + q² = 0 will have solutions x = M² and x = N².

I hope this helps! Let me know if you have any further questions.