Question

An equation is shown. 3x2−8x+4=0

. Complete the statements.(3 points)
The value of a is
3
.

The value of b is
-8
.

The value of c is
4
.

Question 2
9. Using the quadratic equation above, fill in for a, b, and c. (3 points)

-8

-8

3

4

3
Question 3
10. What is one solution of the above quadratic equation?(1 point)
Responses

(1,-1)
(1,-1)

(-0.67,0)
(-0.67,0)

(0,4)
(0,4)

(2,0)
(2,0)

Answer 1

To solve the quadratic equation \(3x^2 - 8x + 4 = 0\), we can use the quadratic formula:

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

We already identified the values of \(a\), \(b\), and \(c\):

- The value of \(a\) is \(3\).
- The value of \(b\) is \(-8\).
- The value of \(c\) is \(4\).

Substituting these values into the quadratic formula:

1. Calculate the discriminant:
\[
b^2 - 4ac = (-8)^2 - 4(3)(4) = 64 - 48 = 16
\]

2. Substitute into the quadratic formula:
\[
x = \frac{-(-8) \pm \sqrt{16}}{2(3)}
\]
\[
x = \frac{8 \pm 4}{6}
\]

3. Calculate the two possible solutions:
- First solution:
\[
x = \frac{8 + 4}{6} = \frac{12}{6} = 2
\]
- Second solution:
\[
x = \frac{8 - 4}{6} = \frac{4}{6} = \frac{2}{3} \approx 0.67
\]

Now, looking at the given response options for Question 3, the solutions would be:

- The solution \( (2, 0) \) corresponds to \(x = 2\).
- The solution \( (-0.67, 0) \) corresponds to \(x \approx 0.67\), which is not an exact match but is close.

Since \(2\) is one of the values we calculated from the equation, the answer to Question 3 is:
**(2, 0)**.