{"status": "success", "data": {"description_md": "How many polynomials of the form $x^5 + ax^4 + bx^3 + cx^2 + dx + 2020$, where $a$, $b$, $c$, and $d$ are real numbers, have the property that whenever $r$ is a root, so is $\\frac{-1+i\\sqrt{3}}{2} \\cdot r$? (Note that $i=\\sqrt{-1}$)\n\n$\\textbf{(A) } 0 \\qquad \\textbf{(B) }1 \\qquad \\textbf{(C) } 2 \\qquad \\textbf{(D) } 3 \\qquad \\textbf{(E) } 4$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>How many polynomials of the form  <span class=\"katex--inline\">x^5 + ax^4 + bx^3 + cx^2 + dx + 2020</span> , where  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> ,  <span class=\"katex--inline\">c</span> , and  <span class=\"katex--inline\">d</span>  are real numbers, have the property that whenever  <span class=\"katex--inline\">r</span>  is a root, so is  <span class=\"katex--inline\">\\frac{-1+i\\sqrt{3}}{2} \\cdot r</span> ? (Note that  <span class=\"katex--inline\">i=\\sqrt{-1}</span> )</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 0 \\qquad \\textbf{(B) }1 \\qquad \\textbf{(C) } 2 \\qquad \\textbf{(D) } 3 \\qquad \\textbf{(E) } 4</span> </p>&#10;<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": 3, "problem_name": "2020 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p18", "prev": "/problem/20_amc12B_p16"}}