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
Neither -1 nor 7 thirds are solutions of 3 x squared minus 4 x minus 4 is equal to 3

Answer 1

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

Rearranging the equation gives us: \[ 3x^2 - 4x - 4 - 3 = 0 \] \[ 3x^2 - 4x - 7 = 0 \]

Next, we can check if -1 and 73 are solutions by substituting them into the equation.

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

2. For \(x = 73\): \[ 3(73)^2 - 4(73) - 7 = 3(5329) - 292 - 7 \] \[ = 15987 - 292 - 7 = 15987 - 299 = 15688 \quad (\text{not } 0) \] So, \(x = 73\) is not a solution.

Thus, the statement "The values -1 and 73 are both solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\)" is False.

Now, for Question 2, since the above statement was false, the correct response would be: "Only -1 is a solution to \(3x^2 - 4x - 4 = 3\)".

So, to summarize:

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