To find the value of the discriminant for the trinomial 2x² + 4x + 2, we first identify the coefficients corresponding to the standard form of a quadratic equation, which is ax² + bx + c.
In this case:
- a = 2
- b = 4
- c = 2
The discriminant (D) can be calculated using the formula:
D = b² – 4ac
Now, substituting the values of a, b, and c into the formula:
D = (4)² – 4(2)(2)
D = 16 – 16
D = 0
Therefore, the value of the discriminant for the trinomial 2x² + 4x + 2 is 0.
A discriminant of zero indicates that the quadratic equation has exactly one real root, meaning the graph of the quadratic touches the x-axis at a single point (a double root).