Question

True or False: The values −1
and 73
are both solutions to the quadratic equation 3x2−4x−4=3
. (2 points)
Responses

True
True

False

Answer 1

To determine whether the values \(-1\) and \(73\) are solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\), we first need to simplify the equation:

1. Subtract \(3\) from both sides:
\[
3x^2 - 4x - 4 - 3 = 0
\]
This simplifies to:
\[
3x^2 - 4x - 7 = 0
\]

Next, we will check both values:

### Checking \(x = -1\):
Substituting \(-1\) into the equation:
\[
3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0
\]
Thus, \(-1\) is a solution.

### Checking \(x = 73\):
Substituting \(73\) into the equation:
\[
3(73)^2 - 4(73) - 7 = 3(5329) - 292 - 7
\]
Calculating this gives:
\[
15987 - 292 - 7 = 15987 - 299 = 15688 \neq 0
\]
Thus, \(73\) is not a solution.

Since \(-1\) is a solution but \(73\) is not, the statement is **False**.