To find the value of b² – 4ac for the quadratic equation x² + 5x + 4 = 0, we first need to identify the coefficients a, b, and c from the standard form of a quadratic equation, which is:
ax² + bx + c = 0
From the given equation:
- a = 1 (coefficient of x²)
- b = 5 (coefficient of x)
- c = 4 (constant term)
Now we can substitute these values into the formula for the discriminant, which is:
b² – 4ac
Plugging in our values we have:
b² – 4ac = 5² – 4(1)(4)
5² = 25
4(1)(4) = 16
Therefore:
b² – 4ac = 25 – 16 = 9.
This means that the value of b² – 4ac for the quadratic equation is 9.