Question

1. True or False: The values -1 and 73
are both solutions to the quadratic equation 3x2−4x−4=3
.

Answer 1

To determine if -1 and 73 are solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\), we first rewrite the equation in standard form by moving all terms to one side:

\[
3x^2 - 4x - 4 - 3 = 0 \implies 3x^2 - 4x - 7 = 0
\]

Now we will test both values, -1 and 73, in the equation \(3x^2 - 4x - 7 = 0\).

1. **Testing \(x = -1\):**

\[
3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0
\]

So, \(x = -1\) is a solution.

2. **Testing \(x = 73\):**

\[
3(73)^2 - 4(73) - 7 = 3(5329) - 292 - 7
\]
\[
= 15987 - 292 - 7
\]
\[
= 15987 - 299 = 15688 \quad (\text{not } 0)
\]

Thus, \(x = 73\) is not a solution.

Since -1 is a solution and 73 is not, the statement "The values -1 and 73 are both solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\)" is **False**.