To determine the number of real solutions for the quadratic equation 2x² + 4x = 0, we can use the discriminant method. A quadratic equation is generally expressed in the form ax² + bx + c = 0, where a, b, and c are constants.
In our equation, we can rewrite it in standard form:
2x² + 4x + 0 = 0
From this equation, we can identify:
- a = 2
- b = 4
- c = 0
The discriminant D is calculated using the formula:
D = b² – 4ac
Now, substituting the values of a, b, and c into the discriminant formula:
D = (4)² – 4(2)(0)
Calculating this gives:
D = 16 – 0 = 16
Now, we interpret the value of the discriminant:
- If D > 0, there are two distinct real solutions.
- If D = 0, there is exactly one real solution (a repeated solution).
- If D < 0, there are no real solutions (the solutions are complex).
Since in our case D = 16, which is greater than zero, we conclude that there are two distinct real solutions for the quadratic equation 2x² + 4x = 0.