Advanced Math practice question

Answer: A. x = −1 ± √5

The equation doesn't factor over the integers, so use the quadratic formula with a = 1, b = 2, c = −4: x = [−2 ± √(4 + 16)] / 2 = [−2 ± √20] / 2 = [−2 ± 2√5] / 2 = −1 ± √5.

Why the other answers are wrong

B. x = 1 ± √5

The sign of −b was dropped: the formula starts with −b = −2, giving −1 after dividing by 2, not +1.

C. x = −2 ± √5

−2 is −b before dividing by 2a = 2. Both parts of the numerator, −2 and ±2√5, get halved.

D. x = −1 ± √3

√3 would need a discriminant of 12. Here b² − 4ac = 4 − 4(1)(−4) = 4 + 16 = 20, and √20 = 2√5.

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