1. True or False: The values -1 and 73

Question

are both solutions to the quadratic equation 3x2−4x−4=3
. (1 point)
Responses

True
True

False
False
Question 2
2. If the above statement was false, which statement below would make it correct?(1 point)
Responses

The above statement was true
The above statement was true

Only -1 is a solution to 3x2−4x−4=3
Only -1 is a solution to 3 x squared minus 4 x minus 4 is equal to 3

Only 73
is a solution of 3x2−4x−4=3
Only 7 thirds is a solution of 3 x squared minus 4 x minus 4 is equal to 3

Neither -1 nor 73
are solutions of 3x2−4x−4=3

Answer 1

To determine whether the statement is true or false, we first need to solve the equation \(3x^2 - 4x - 4 = 3\).

1. Rearranging the equation:
   \(3x^2 - 4x - 4 - 3 = 0\)
   \(3x^2 - 4x - 7 = 0\).

Next, we will check if -1 and 73 are solutions by substituting these values into the equation \(3x^2 - 4x - 7 = 0\).

Checking -1: \[ 3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0. \] So, -1 is indeed a solution.

Checking 73: \[ 3(73)^2 - 4(73) - 7. \] Calculating each term: \(3(73^2) = 3(5329) = 15987\),
\(-4(73) = -292\),
and then summing: \[ 15987 - 292 - 7 = 15987 - 299 = 15688 \neq 0. \] So, 73 is not a solution.

Based on this:

1. The statement "The values -1 and 73 are both solutions to the quadratic equation" is False.

For question 2, since the original statement was false because only -1 is a solution, the correct response would be:

Only -1 is a solution to \(3x^2 - 4x - 4 = 3\).