Question
A student was asked to use the quadratic formula to solve the following equation. Which answer shows them settingthe problem up
Correctly
?
2
x
2
−
5
x
=
1
(10 points)
x =
5 ± √− 25 + 8
4
x =
5 ± √25 − 8
4
x =
5 ± √− 25 − 8
4
x =
5 ± √25 + 8
4
Correctly
?
2
x
2
−
5
x
=
1
(10 points)
x =
5 ± √− 25 + 8
4
x =
5 ± √25 − 8
4
x =
5 ± √− 25 − 8
4
x =
5 ± √25 + 8
4
Answers
GPT-5 mini
First write in standard form: 2x^2 − 5x − 1 = 0, so a = 2, b = −5, c = −1.
Quadratic formula: x = [−b ± √(b^2 − 4ac)]/(2a) = [5 ± √(25 − 4·2·(−1))]/4 = [5 ± √(25 + 8)]/4.
So the correct choice is the fourth option (x = (5 ± √(25 + 8))/4), which simplifies to x = (5 ± √33)/4.
Quadratic formula: x = [−b ± √(b^2 − 4ac)]/(2a) = [5 ± √(25 − 4·2·(−1))]/4 = [5 ± √(25 + 8)]/4.
So the correct choice is the fourth option (x = (5 ± √(25 + 8))/4), which simplifies to x = (5 ± √33)/4.