Question

Помогите пожалуйста,,,Является ли число -1 корнем уравнения х2 - 4х - 5 = 0?

Answer 1

Является, так как:
(-1)² -4 · (-1) - 5 = 0
1 + 4 - 5 = 0
5 - 5 = 0

Так же:
х² - 4х - 5 = 0
D = 4² -4 · (-5) · 1 = 16 + 20 = 36
x₁ = (4 + 6)/2 = 5
x₂ = (4 - 6)/2 = -1

Answer 2

Checking if -1 is a Root of the Equation

To determine if -1 is a root of the equation \(x^2 - 4x - 5 = 0\), we can substitute -1 for x in the equation and check if the equation holds true.

Substituting -1 for x in the equation: \[(-1)^2 - 4(-1) - 5 = 1 + 4 - 5 = 0\]

The result is 0, which means that -1 is a root of the equation.

Conclusion: - Yes, -1 is a root of the equation \(x^2 - 4x - 5 = 0\).