The discriminant of a quadratic equation of the form ax² + bx + c is calculated using the formula D = b² – 4ac.
In this case, we identify the coefficients from the trinomial:
- a = 3
- b = 6
- c = 5
Now, we can substitute these values into the discriminant formula:
D = (6)² – 4(3)(5)
Calculating step-by-step:
- (6)² = 36
- 4 × 3 × 5 = 60
Now, substitute back into the discriminant formula:
D = 36 – 60
This simplifies to:
D = -24
So, the value of the discriminant for the trinomial 3x² + 6x + 5 is -24.
A negative value for the discriminant indicates that the quadratic equation does not have real roots, meaning the parabola does not intersect the x-axis.