The discriminant of a quadratic equation is a key element that helps us understand the nature of its roots. For a quadratic equation of the form ax² + bx + c = 0, the discriminant D is given by the formula:
D = b² – 4ac
In your equation 9x² + 10x + 2, we can identify the coefficients as:
- a = 9
- b = 10
- c = 2
Now, substituting these values into the formula for the discriminant:
D = (10)² – 4 × (9) × (2)
D = 100 – 72
D = 28
The discriminant D = 28 is positive. This indicates that the quadratic equation has two distinct real roots. A positive discriminant is always a good sign when solving equations, as it confirms that the roots can be found on the real number line.