Use the discriminant to determine the number of real solutions of −6x2−108=0

To determine the number of real solutions for the equation \(-6x^2 - 108 = 0\), we can first rewrite it in standard quadratic form \(ax^2 + bx + c = 0\):

\[ -6x^2 + 0x - 108 = 0 \]

Here, \(a = -6\), \(b = 0\), and \(c = -108\).

The discriminant (D) is calculated using the formula:

\[ D = b^2 - 4ac \]

Substituting the values of \(a\), \(b\), and \(c\):

\[ D = 0^2 - 4(-6)(-108) \] \[ D = 0 - 4 \times -6 \times -108 \] \[ D = -4 \times 6 \times 108 \] \[ D = -2592 \]

Since the discriminant \(D\) is negative (\(-2592 < 0\)), this indicates that there are no real solutions.

Therefore, the correct statement is:

There will be no real solutions since the discriminant is negative.