AMC 10B 2023 (Problem 22)
How many distinct values of satisfy , where denotes the greatest integer less than or equal to ?
Let , where and . Then .
By Toolkit 31 — Signs and Roots of Quadratics,
Since is the integer part of , from this part can be any integer.
By Hint 4,
By Toolkit 21 — Quadratic Formula, the roots of are
By Toolkit 31 — Signs and Roots of Quadratics,
Since is an integer,
By Toolkit 21 — Quadratic Formula, the roots of are
By Toolkit 31 — Signs and Roots of Quadratics,
Since is an integer,
(B)