The discriminant of a quadratic equation is a key component that helps determine the nature of the roots of the equation. For a standard quadratic equation of the form ax² + bx + c = 0, the discriminant can be calculated using the formula:
D = b² – 4ac
In your case, the quadratic equation is 9x² + 10x + 2. Here, we can identify the coefficients:
- a = 9
- b = 10
- c = 2
Now, we can substitute these values into the discriminant formula:
D = (10)² – 4(9)(2)
D = 100 – 72
D = 28
The discriminant D = 28 is a positive value, which indicates that the quadratic equation 9x² + 10x + 2 has two distinct real roots. In summary, the discriminant not only serves as a useful tool for understanding the roots of the equation but also provides deeper insights into the properties of the quadratic functions!