To solve the quadratic expression 4x² + 9x + 4, you can apply the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / (2a)
In this expression, the parameters are defined as follows:
- a = 4 (the coefficient of x²)
- b = 9 (the coefficient of x)
- c = 4 (the constant term)
Next, we need to calculate the discriminant, which is b² – 4ac:
Discriminant = 9² – 4 * 4 * 4
Discriminant = 81 – 64 = 17
Since the discriminant is positive, we will have two real and distinct solutions. Now we can substitute the values of a, b, and the discriminant into the quadratic formula:
x = (-9 ± √17) / (2 * 4)
This simplifies to:
x = (-9 ± √17) / 8
Thus, the two solutions for the equation 4x² + 9x + 4 = 0 are:
x₁ = (-9 + √17) / 8
x₂ = (-9 – √17) / 8
In conclusion, the expression 4x² + 9x + 4 has two real roots calculated using the quadratic formula, providing valuable insights into its behavior as a function.