Use the discriminant to determine the number of real solutions of -6x^2-108=0 which of the following statements gives the correct explanation? (1 point)
There will be no real solutions since the discriminant is negative.
There will be two real solutions since the discriminant is positive.
There will be no real solutions since the discriminant is zero.
There will be one real solution since the discriminant is zero.
There will be two real solutions since the discriminant is positive.
The discriminant can be calculated using the formula:
Discriminant = b^2 - 4ac
In the given equation -6x^2 - 108 = 0, a = -6, b = 0, and c = -108.
Substituting these values into the discriminant formula, we get:
Discriminant = (0)^2 - 4(-6)(-108) = 0 - (4)(6)(-108) = 0 - (-2592) = 0 + 2592 = 2592.
Since the discriminant (2592) is positive, the correct statement is:
There will be two real solutions since the discriminant is positive.
To determine the number of real solutions of a quadratic equation, we can use the discriminant. The discriminant is calculated as b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, the quadratic equation is -6x^2 - 108 = 0. By comparing it to the standard form, we have a = -6, b = 0, and c = -108.
Now let's find the discriminant:
Discriminant = b^2 - 4ac
Discriminant = 0^2 - 4(-6)(-108)
Discriminant = 0 - 4(648)
Discriminant = 0 - 2592
Discriminant = -2592
Based on the discriminant, we can determine the number of real solutions:
- If the discriminant is positive, there are two distinct real solutions.
- If the discriminant is negative, there are no real solutions.
- If the discriminant is zero, there is one real solution.
In this case, the discriminant is negative (-2592), so the correct explanation is: "There will be no real solutions since the discriminant is negative."