The discriminant of a quadratic equation is a value that helps determine the nature of the roots of the equation. For the standard form of a quadratic equation, which is given by ax² + bx + c = 0, the discriminant (D) is calculated using the formula:
D = b² – 4ac
In the equation x² + 4x + 2 = 0, we can identify the coefficients as follows:
- a = 1
- b = 4
- c = 2
Now, we plug these values into the discriminant formula:
D = (4)² – 4(1)(2)
D = 16 – 8
D = 8
The discriminant is 8. This positive value indicates that the quadratic equation has two distinct real roots. Since the discriminant is not zero, it confirms that the roots are not equal.