{"id":"cb_question_bank:613e3442-9911-4b8a-807c-26282c523908","source_id":"cb_question_bank","source_item_id":"613e3442-9911-4b8a-807c-26282c523908","external_id":"c324ef1d-80fd-41a5-9609-8658df690543","ibn":null,"question_id":"71014fb1","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"left parenthesis x minus 1 right parenthesis squared equals negative 4 How many distinct real solutions does the given equation have?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"left parenthesis x minus 1 right parenthesis squared equals negative 4\"><mrow>\n\t<msup>\n\t\t<mfenced>\n\t\t\t<mrow>\n\t\t\t\t<mi>x</mi>\n\t\t\t\t<mo>-</mo>\n\t\t\t\t<mn>1</mn>\n\t\t\t</mrow>\n\t\t</mfenced>\n\t\t<mn>2</mn>\n\t</msup>\n\t<mo>=</mo>\n\t<mo>-</mo><mn>4</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">How many distinct real solutions does the given equation have?</p>","rationale_html":"<p>Choice D is correct. Any quantity that is positive or negative in value has a positive value when squared. Therefore, the left-hand side of the given equation is either positive or zero for any value of <math><mi>x</mi>\n</math>. Since the right-hand side of the given equation is negative, there is no value of <math><mi>x</mi>\n</math> for which the given equation is true. Thus, the number of distinct real solutions for the given equation is zero.</p>\n<p>Choices A, B, and C are incorrect and may result from conceptual errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.824000+00:00","source_updated_at":"2023-08-02T20:25:59.824000+00:00","options":[{"label":"A","content_html":"<p>Exactly one</p>","ord":0},{"label":"B","content_html":"<p>Exactly two</p>","ord":1},{"label":"C","content_html":"<p>Infinitely many</p>","ord":2},{"label":"D","content_html":"<p>Zero</p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}