{"id":"cb_practice_pdf:t5-math-m2-q24","source_id":"cb_practice_pdf","source_item_id":"t5-math-m2-q24","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-5","module_number":2,"position":24,"stem":"Which quadratic equation has no real solutions? +14x−49 = 0","stimulus":"","stimulus_html":null,"stem_html":"<p>Which quadratic equation has no real solutions? +14x−49 = 0</p>","rationale_html":"<p>Choice D is correct. The number of solutions to a quadratic equation in the form 2+ + =0 ax bx c , where a, b, and c are constants, can be determined by the value 2-4 of the discriminant, b ac. If the value of the discriminant is greater than zero, then the quadratic equation has two distinct real solutions. If the value of the discriminant is equal to zero, then the quadratic equation has exactly one real solution. If the value of the discriminant is less than zero, then the quadratic equation has no real solutions. For the quadratic equation in choice D, 5 2-14 +49=0 = =-14 =49 -14 x x , a 5, b , and c . Substituting 5 for a, for b, 49 2-4 -14 2-4 5 49 -784 -784 and for c in b ac yields ^ h ^ h^ h, or . Since is less 5 2-14 +49=0 than zero, it follows that the quadratic equation x x has no real solutions. 48 SAT PRACTICE TEST #5 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 Choice A is incorrect. The value of the discriminant for this quadratic equation is 392 392 . Since is greater than zero, it follows that this quadratic equation has two real solutions. Choice B is incorrect. The value of the discriminant for this quadratic equation is 0. Since zero is equal to zero, it follows that this quadratic equation has exactly one real solution. Choice C is incorrect. The value of the 1,176 1,176 discriminant for this quadratic equation is . Since is greater than zero, it follows that this quadratic equation has two real solutions.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>x^2</p>","ord":0},{"label":"B","content_html":"<p>x^2 −14x+49 = 0 5x^2 −14x−49 = 0</p>","ord":1},{"label":"C","content_html":"","ord":2},{"label":"D","content_html":"<p>5x^2 −14x+49 = 0</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}