Question

Скласти квадратне рівняння з цілими коефіцієнтами, корені якого 3 і 4

Answer 1

Відповідь:

Пояснення:

3+4 = 7

3*4 = 12

x^2 - 7x + 12 = 0

(Використовуємо т. Вієта :

х1+х2=-b

x1x2=c)

Answer 2

Solving a Quadratic Equation with Integer Coefficients and Roots 3 and 4

To solve a quadratic equation with integer coefficients and roots 3 and 4, we can use the general form of a quadratic equation: ax^2 + bx + c = 0, where a, b, and c are the coefficients of the quadratic equation.

Given that the roots are 3 and 4, we can use the fact that the sum of the roots of a quadratic equation x^2 - (sum of roots)x + product of roots = 0. Therefore, the sum of the roots is 3 + 4 = 7, and the product of the roots is 3 * 4 = 12.

Using this information, we can construct the quadratic equation as follows:

1. The sum of the roots is 7, so the coefficient of the linear term (b) is -7. 2. The product of the roots is 12, so the constant term (c) is 12.

Therefore, the quadratic equation is x^2 - 7x + 12 = 0.

Using the Quadratic Formula

We can also solve the quadratic equation using the quadratic formula, which states that for a quadratic equation ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, the coefficients are: - a = 1 - b = -7 - c = 12

Substituting these values into the quadratic formula, we get:

x = (-(-7) ± √((-7)^2 - 4*1*12)) / (2*1)

Solving further: x = (7 ± √(49 - 48)) / 2 x = (7 ± √1) / 2 x = (7 ± 1) / 2

So, the solutions are: x = (7 + 1) / 2 = 8 / 2 = 4 x = (7 - 1) / 2 = 6 / 2 = 3

Therefore, the quadratic equation x^2 - 7x + 12 = 0 has roots 3 and 4.