Question

X2-x-20=0 Через дискриминант

Answer 1

Решение:
$x^2-x-20=0\\D=b^2-4ac=1+80=81\\x_{1,2}=\frac{-b\pm\sqrt{D}}{2a}\\x_1=\frac{1+9}{2}=5\\x_2=\frac{1-9}{2}=-4$
Ответ: -4 и 5

Answer 2

Solving the Equation x^2 - x - 20 = 0 using the Discriminant

To solve the equation x^2 - x - 20 = 0 using the discriminant, we need to find the values of x that satisfy the equation. The discriminant is a mathematical term used to determine the nature of the solutions of a quadratic equation.

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. In this case, the equation is x^2 - x - 20 = 0, so a = 1, b = -1, and c = -20.

The discriminant (D) is calculated using the formula D = b^2 - 4ac. If the discriminant is greater than zero (D > 0), the equation has two distinct real solutions. If the discriminant is equal to zero (D = 0), the equation has one real solution. If the discriminant is less than zero (D < 0), the equation has no real solutions.

Let's calculate the discriminant for the equation x^2 - x - 20 = 0:

D = (-1)^2 - 4 * 1 * (-20) = 1 + 80 = 81

Since the discriminant is greater than zero (D > 0), the equation has two distinct real solutions.

To find the solutions, we can use the quadratic formula:

x1 = (-b + √D) / (2a) x2 = (-b - √D) / (2a)

Plugging in the values, we get:

x1 = (-(-1) + √81) / (2 * 1) = (1 + 9) / 2 = 10 / 2 = 5 x2 = (-(-1) - √81) / (2 * 1) = (1 - 9) / 2 = -8 / 2 = -4

Therefore, the solutions to the equation x^2 - x - 20 = 0 are x = 5 and x = -4.

Answer: The solutions to the equation x^2 - x - 20 = 0, obtained using the discriminant, are x = 5 and x = -4.