Question

Use the table to answer the question.

x Substituted Evaluate True Statement?
−14

13

1

For the quadratic equation −3x2−2x+1=0
, complete the table by testing each of the given values to determine whether it is a solution. Identify which one of the values is in the solution set. Enter your answer as a fraction.

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Responses

Only x=−14
is in the solution set.
Only x is equal to negative 1 fourth is in the solution set.

Only x=13
is in the solution set.
Only x is equal to 1 third is in the solution set.

Only x=1
is in the solution set.

Answer 1

Evaluate −3x^2 − 2x + 1 for each given x:

- x = −14: −3(−14)^2 − 2(−14) + 1 = −3(196) + 28 + 1 = −588 + 29 = −559 ≠ 0
- x = 13: −3(13)^2 − 2(13) + 1 = −3(169) − 26 + 1 = −507 − 25 = −532 ≠ 0
- x = 1: −3(1)^2 − 2(1) + 1 = −3 − 2 + 1 = −4 ≠ 0

Solve the quadratic: 3x^2 + 2x − 1 = 0 → x = [−2 ± √(4 + 12)]/6 = (−2 ± 4)/6, so x = 1/3 or x = −1.

The value in the solution set (as a fraction) is 1/3.