Determine whether the values −1 and 73 are solutions to the quadratic equation 3x2−4x−4=3 .(1 point)

Question

Determine whether the values  −1  and  73  are solutions to the quadratic equation  3x2−4x−4=3 .(1 point)
Responses

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.

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.

GPT-4o mini · Answer

To determine whether the values $ x = -1 $ and $ x = 73 $ are solutions to the quadratic equation $ 3x^2 - 4x - 4 = 3 $, we first rewrite the equation as: $$ 3x^2 - 4x - 4 - 3 = 0 $$ which simplifies to: $$ 3x^2 - 4x - 7 = 0 $$ Next, we'll check if $ x = -1 $ and $ x = 73 $ satisfy this equation. **Checking $ x = -1 $:** Substituting $ x = -1 $: $$ 3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0 $$ So, $ x = -1 $ is a solution. **Checking $ x = 73 $:** Substituting $ x = 73 $: $$ 3(73)^2 - 4(73) - 7 = 3(5329) - 292 - 7 = 15987 - 292 - 7 = 15987 - 299 = 15688 \neq 0 $$ So, $ x = 73 $ is not a solution. Given this analysis, we conclude: Only $ x = -1 $ is a solution.