{"status": "success", "data": {"description_md": "How many distinct values of $x$ satisfy\n$\\lfloor{x}\\rfloor^2-3x+2=0,$ \nwhere $\\lfloor{x}\\rfloor$ denotes the largest integer less than or equal to $x$?\n\n$\\textbf{(A) } \\text{an infinite number} \\qquad \\textbf{(B) } 4 \\qquad \\textbf{(C) } 2 \\qquad \\textbf{(D) } 3 \\qquad \\textbf{(E) } 0$", "description_html": "<p>How many distinct values of  <span class=\"katex--inline\">x</span>  satisfy<br/>\n <span class=\"katex--inline\">\\lfloor{x}\\rfloor^2-3x+2=0,</span> <br/>\nwhere  <span class=\"katex--inline\">\\lfloor{x}\\rfloor</span>  denotes the largest integer less than or equal to  <span class=\"katex--inline\">x</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } \\text{an infinite number} \\qquad \\textbf{(B) } 4 \\qquad \\textbf{(C) } 2 \\qquad \\textbf{(D) } 3 \\qquad \\textbf{(E) } 0</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2023 AMC 10B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10B_p23", "prev": "/problem/23_amc10B_p21"}}