Question

What is the solution set for x2−x−72=0
?

(1 point)

{−9,−8}

{−4,9}

{−8,9}

{4,9}

And for the wrong solutions, what mistake would you have to make to get that answer

Answer 1

Solve: x^2 − x − 72 = 0.

Factor: (x − 9)(x + 8) = 0, so x = 9 or x = −8. Solution set: {−8, 9}.

How the wrong choices could arise:
- {−9, −8}: factoring as (x + 9)(x + 8) — i.e. using +72 instead of −72 (wrong sign for the constant).
- {−4, 9}: using factors −4 and 9 (which give −36), i.e. mistakenly using −36 instead of −72 (for example, halving the constant by accident).
- {4, 9}: using factors 4 and 9 (which give +36), i.e. both sign and magnitude errors (e.g. changing −72 to +36).

(Using the quadratic formula gives x = (1 ± √289)/2 = (1 ± 17)/2 = 9 and −8, confirming the correct roots.)