Answer:
1) Value of Discriminant: -32
Solution Value(s):
x = -2/3 + 2√2i/3
x = -2/3 - 2√2i/3
2) Value of Discriminant: -44
Solution Value(s):
x = -1/3 + √11i/3
x = -1/3 - √11i/3
Explanation:
The Discriminant is the part of the Quadratic Formula that is under the square root symbol.
If the Discriminant > 0 there are 2 real solutions.
If the Discriminant = 0 there is 1 real solution.
If the Discriminant < 0 there are 2 imaginary solutions.
Equation 1:
3x² + 4x + 4 = 0
Plug this into the Quadratic Formula and solve:
x = -4 ± √-32 all over 6
Value of Discriminant: -32
Obviously, this can be simplified more, but for now, all you need is what is under the square root. Since it is less than 0, there are going to be 2 imaginary solutions.
Continue simplifying to get to the Solution Values. You will end up here:
x = -2/3 ± 2√2i/3
Your two imaginary solutions are:
x = -2/3 + 2√2i/3
x = -2/3 - 2√2i/3
*Note: 2√2i is ALL over 3, not just the √2i*
You can convert this to decimal if you need (but I don’t suggest it):
x = -0.66666 + 0.942809i
x = -0.66666 - 0.942809i
Equation 2:
3x² + 2x + 4 = 0
Plug this into the Quadratic Formula and solve:
x = -2 ± √-44 all over 6
Value of Discriminant: -44
Obviously, this can be simplified more, but for now, all you need is what is under the square root. Since it is less than 0, there are going to be 2 imaginary solutions again.
Continue simplifying to get to the Solution Values. You will end up here:
x = -1/3 ± √11i/3
Your two imaginary solutions are:
x = -1/3 + √11i/3
x = -1/3 - √11i/3
You can convert this to decimal if you need (but I don’t suggest it):
x = -0.33333 + 1.10554i
x = -0.33333 - 1.10554i
Hope this helps!