The discriminant of a quadratic equation is a key value that helps us determine the nature of the roots of the equation. For a standard quadratic equation of the form ax² + bx + c = 0, the discriminant (D) is calculated using the formula:
D = b² – 4ac
In your case, the quadratic equation is incorrectly stated. The standard form should be organized correctly. Let’s rewrite it to fit the quadratic format. Assuming you meant 5x² + 2x + 1 = 0, here:
- a = 5
- b = 2
- c = 1
Now we can plug these values into the discriminant formula:
D = (2)² – 4(5)(1)
D = 4 – 20 = -16
The discriminant value of -16 indicates that the roots of the quadratic equation are complex numbers, meaning there are no real solutions. In summary, if you have a quadratic equation in standard form, you can find its discriminant and interpret the nature of its roots accordingly.