What is the discriminant of the function f(x) = 5x² + 36x + 54?

To find the discriminant of a quadratic function given in the form ( f(x) = ax^2 + bx + c ), we use the formula for the discriminant, ( D = b^2 - 4ac ). In this case, the coefficients from the function ( f(x) = 5x^2 + 36x + 54 ) are:

• ( a = 5 )

• ( b = 36 )

• ( c = 54 )

Now, substituting these values into the discriminant formula:

1. First, calculate ( b^2 ):

[

b^2 = 36^2 = 1296

]

2. Next, calculate ( 4ac ):

[

4ac = 4 \times 5 \times 54 = 1080

]

3. Now, we find ( D ) by subtracting ( 4ac ) from ( b^2 ):

[

D = 1296 - 1080 = 216

]

Therefore, the discriminant of the function ( f(x) = 5x^2 + 36x