Question

Question 1 A)Determine whether the values −1 and 73 are solutions to the quadratic equation 3x2−4x−4=3 .(1 point) Responses Both x=−1 and x=73 are solutions. Both x equals negative 1 and x equals Start Fraction 7 over 3 End Fraction are solutions. Neither x=−1 nor x=73 is a solution. Neither x equals negative 1 nor x equals Start Fraction 7 over 3 End Fraction is a solution. Only x=73 is a solution. Only x equals Start Fraction 7 over 3 End Fraction is a solution. Only x=−1 is a solution. Only x equals negative 1 is a solution.

Answer 1

To determine whether the values -1 and 73 are solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\), we first rearrange the equation into the standard form of a quadratic equation:

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

Next, we can substitute the values -1 and 73 into the equation to see if they satisfy it.

1. For \(x = -1\): \[ 3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0 \] Since the left side equals 0, \(x = -1\) is a solution.

2. For \(x = 73\): \[ 3(73)^2 - 4(73) - 7 = 3(5329) - 292 - 7 = 15987 - 292 - 7 = 15987 - 299 = 15688 \] Since the left side does not equal 0, \(x = 73\) is not a solution.

Based on this evaluation, the results are:

• \(x = -1\) is a solution.
• \(x = 73\) is not a solution.

Therefore, the correct response is: Only \(x = -1\) is a solution.