Consider only the discriminant, b2 - 4ac, to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions. 2x2 = -2 -5

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Are you missing an x?

2x^2 + 2x + 5 = 0

a = 2
b=2
c = 5

If your answer = 0 then there is only 1 real number solution.

If your answer = any positive number you will have two real solutions

If your answer = any negative number you will have two imaginary solutions.

All of the above happens because in the quadratic equation you take +/- the square root of b^2-4ac

What is the commutative law of addition to find an expressoon equivalent to 5m + 9n

To determine the nature of the solutions, we need to look at the discriminant, which is given by b^2 - 4ac. In this case, the quadratic equation we have is 2x^2 = -2 - 5.

By comparing with the standard form of a quadratic equation, ax^2 + bx + c = 0, we can see that:
a = 2, b = 0, and c = -2 - 5 = -7.

Now, we can calculate the discriminant:
b^2 - 4ac = (0)^2 - 4(2)(-7) = 0 + 56 = 56.

Since the discriminant (56) is positive, the quadratic equation has two different real-number solutions.

To determine the number and type of solutions to the quadratic equation 2x^2 = -2 - 5, we can start by rewriting the equation in standard form, where the quadratic term (x^2) is positive:

2x^2 + 7 = 0

Now we can identify the coefficients a, b, and c for the general form of the quadratic equation: ax^2 + bx + c = 0:

a = 2
b = 0 (no x-term)
c = 7

Next, we can calculate the discriminant using the formula b^2 - 4ac. The discriminant determines the nature of the solutions:

Discriminant = b^2 - 4ac

Substituting the values:
Discriminant = (0)^2 - 4(2)(7)
Discriminant = 0 - 56
Discriminant = -56

Now, based on the value of the discriminant, we can determine the nature of the solutions:

1. If the discriminant is greater than 0, there are two different real-number solutions.
- In this case, since the discriminant is negative (-56), we don't have two different real-number solutions.

2. If the discriminant is equal to 0, there is one real-number solution.
- In this case, the discriminant is not equal to zero, so we don't have one real-number solution.

3. If the discriminant is less than 0, there are two different imaginary-number solutions.
- Since the discriminant is negative (-56), we have two different imaginary-number solutions.

Therefore, the quadratic equation 2x^2 + 7 = 0 has two different imaginary-number solutions.