To find the discriminant of the trinomial 3x² + 6x + 5, we first need to recall the formula for the discriminant, which is derived from the quadratic equation in the standard form, ax² + bx + c. The discriminant (D) is given by:
D = b² – 4ac
In this trinomial, the coefficients are:
- a = 3
- b = 6
- c = 5
Now, we can plug these values into the discriminant formula:
D = (6)² – 4(3)(5)
Calculating the first part:
(6)² = 36
Now for the second part:
4(3)(5) = 60
Now, we substitute these values back into our discriminant formula:
D = 36 – 60
This simplifies to:
D = -24
Since the discriminant is negative (-24), it indicates that the trinomial 3x² + 6x + 5 has no real roots and therefore the corresponding quadratic equation does not intersect the x-axis.
In conclusion, the value of the discriminant for the given trinomial is -24.