What is the discriminant of the quadratic equation \( 2x^2 + 4x + 6 = 0 \)?

To find the discriminant of the quadratic equation ( 2x^2 + 4x + 6 = 0 ), we use the discriminant formula given by ( D = b^2 - 4ac ), where ( a ), ( b ), and ( c ) are the coefficients of the quadratic equation in the standard form ( ax^2 + bx + c = 0 ).

In the given equation, the coefficients are:

• ( a = 2 )

• ( b = 4 )

• ( c = 6 )

Now, we can substitute these values into the discriminant formula:

[

D = (4)^2 - 4(2)(6)

]

Calculating ( (4)^2 ) gives us ( 16 ).

Next, we calculate ( 4(2)(6) ):

[

4 \times 2 = 8

]

[

8 \times 6 = 48

]

Now, substituting these results back into the formula gives:

[

D = 16 - 48

]

Calculating ( 16 - 48 ) results in:

[

D = -32