Use the quadratic formula to complete the table. To verify your solutions, graph the equations. thank you so much for your help :)

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

Step-by-step 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!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

you could deduce the conclusion directly using the facts pertaining to the specific situation.

hope this .