Question

Using the quadratic equation above, fill in for a, b, and c.
-___ ± √___^2 -4 (__)(__)
_____________________
2(__)
the options for all blanks are x, 1, 3, or 4

Answer 1

What is one solution of the above quadratic equation?(1 point)
Responses

(-3,0)
(-3,0)

(-4,0)
(-4,0)

(0,3)
(0,3)

(-2,-1)

Answer 2

To fill in the blanks for the quadratic formula, we first need to understand the general form of a quadratic equation:

\[ ax^2 + bx + c = 0 \]

The corresponding values for the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Now we can fill in the blanks using the options provided (x, 1, 3, or 4):

1. In the formula \( -b \), \( b \) can be either x, 1, 3, or 4. We’ll use the simplest option, which is:
- **Fill in the first blank with:** **1**

2. The expression under the square root \( b^2 - 4ac \) requires us to fill in:
- **\( b = 1 \) fills in the second blank: \[1^2\]**
- Choose \( a = 1 \) and \( c = 3 \) for this example.
- **Fill in the third blank with:** **3** (for \( c \))
- **Fill in the fourth blank with:** **1** (for \( a \))

3. The denominator \( 2a \):
- Since we used \( a = 1 \),
- **Fill in the last blank with:** **1**

Putting this together, your completed quadratic formula will be:

\[
-1 \pm \sqrt{1^2 - 4(1)(3)}
\]
\[
\frac{-1 \pm \sqrt{1}}{2(1)}
\]

So the final filled-in version is:

\[
-1 \pm \sqrt{1^2 - 4 (1)(3)}
\]
\[
\frac{-1 \pm \sqrt{1}}{2(1)}
\]

Keep in mind that there could be other combinations of values for \( a \), \( b \), and \( c \) depending on your specific needs or preferences!

Answer 3

To find one solution of the quadratic equation given in the form:

\[
-1 \pm \sqrt{1^2 - 4(1)(3)}
\]

First, we simplify the expression under the square root:

1. Calculate \( 1^2 - 4(1)(3) \):
\[
1 - 12 = -11
\]

So, the quadratic equation turns into:

\[
x = \frac{-1 \pm \sqrt{-11}}{2}
\]

Since \(\sqrt{-11}\) indicates that the solutions will be complex (involving imaginary numbers), they cannot have real-number solutions. Therefore, none of the provided responses can be solutions to this particular quadratic equation.

However, let's analyze the provided options one more time for any possible connection:

- **(-3, 0)**: Corresponds to the x-intercept at x = -3 (not a solution to the quadratic).
- **(-4, 0)**: Corresponds to the x-intercept at x = -4 (not a solution).
- **(0, 3)**: Corresponds to y = 3 when x = 0 (not a solution).
- **(-2, -1)**: Also not an x-intercept.

Since the original quadratic equation yields complex solutions, none of the given responses are actual solutions.

If you have any specific additional context or a different equation in mind, please provide it, and I would be happy to assist further!