Question

При каком значении а уравнение 2х^2 + 4x + a = 0 имеет один корень? Найдите этот корень.

Answer 1

Чтобы уравнение имело один корень дискриминант должен быть равен нулю  
D=16-4*2*а
16-8а=0
-8а=-16
а=16/8
а=2
при а=2 уравнение имеет 1 корень 

Answer 2

Solving the Equation for a Single Root

To find the value of a for which the equation 2x^2 + 4x + a = 0 has a single root, we can use the discriminant of the quadratic equation. The discriminant is given by the formula b^2 - 4ac. When the discriminant is equal to 0, the quadratic equation has a single real root.

Calculating the Discriminant

The discriminant for the given quadratic equation is calculated as follows: b^2 - 4ac = 4^2 - 4*2*a = 16 - 8a

Finding the Value of a

For the equation to have a single root, the discriminant should be equal to 0: 16 - 8a = 0 Solving for a: 16 = 8a a = 2

Therefore, the value of a for which the equation 2x^2 + 4x + a = 0 has a single root is a = 2.

Conclusion

The value of a that results in the equation having a single root is a = 2.