1. Find the solutions to the following equations: 1) Solve the equation 5x2 − 10 = 0; 3) Determine the values of
1. Find the solutions to the following equations: 1) Solve the equation 5x2 − 10 = 0; 3) Determine the values of x in the equation x2 + 6x − 7 = 0; 5) Solve for x in the equation x2 − 3x + 1 = 0; 2) Find the roots of the equation 3x2 + 4x = 0; 4) Determine the solutions to the equation 3x2 + 7x + 2 = 0; 6) Solve the equation x2 − x + 3 = 0.
2. Create a quadratic equation where the sum of the roots is equal to 6 and the product is equal to 4.
3. One side of a rectangle is 7 cm longer than the other. Find the lengths of the sides if the area of the rectangle is 44 cm2.
4. The number -6 is one of the roots of the equation 2x2 + bx − 6 = 0. Find the second root of the equation and the value of b.
5. For what value of a does the equation 2x2 + 4x + a = 0 have a single root?
6. It is known that
2. Create a quadratic equation where the sum of the roots is equal to 6 and the product is equal to 4.
3. One side of a rectangle is 7 cm longer than the other. Find the lengths of the sides if the area of the rectangle is 44 cm2.
4. The number -6 is one of the roots of the equation 2x2 + bx − 6 = 0. Find the second root of the equation and the value of b.
5. For what value of a does the equation 2x2 + 4x + a = 0 have a single root?
6. It is known that
25.11.2023 19:20
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1) Решим уравнение 5x^2 - 10 = 0:
5x^2 - 10 = 0
5x^2 = 10
x^2 = 10/5
x^2 = 2
x = √2 или x = -√2
2) Определим значения x в уравнении x^2 + 6x - 7 = 0:
x^2 + 6x - 7 = 0
(x + 7)(x - 1) = 0
x + 7 = 0 или x - 1 = 0
x = -7 или x = 1
3) Найдем значения x в уравнении x^2 - 3x + 1 = 0:
Используем квадратное уравнение или найдем корни с помощью дискриминанта:
x = (-b ± √(b^2 - 4ac)) / 2a
В данном уравнении a = 1, b = -3, c = 1:
x = (3 ± √((-3)^2 - 4*1*1)) / 2*1
x = (3 ± √(9 - 4)) / 2
x = (3 ± √5) / 2
Таким образом, уравнение имеет два решения: x = (3 + √5) / 2 и x = (3 - √5) / 2.
4) Найдем корни уравнения 3x^2 + 4x = 0:
3x^2 + 4x = 0
x(3x + 4) = 0
x = 0 или 3x + 4 = 0
x = 0 или 3x = -4
x = 0 или x = -4/3
5) Решим уравнение 3x^2 + 7x + 2 = 0:
3x^2 + 7x + 2 = 0
(3x + 1)(x + 2) = 0
3x + 1 = 0 или x + 2 = 0
x = -1/3 или x = -2
6) Решим уравнение x^2 - x + 3 = 0:
x^2 - x + 3 = 0
(x - 1/2)^2 + 11/4 = 0
(x - 1/2)^2 = -11/4
Уравнение не имеет действительных корней, так как квадрат не может быть отрицательным числом.
Дополнительный материал: Решите уравнение 2x^2 - 4 = 0.
Совет: Для решения квадратных уравнений, можно использовать квадратное уравнение или метод дискриминанта.
Закрепляющее упражнение: Решите уравнение 4x^2 + 9 = 0.