{"id":"aqua_rat:0d4e8bbf6665de497184bc0c9354e209","source_id":"aqua_rat","source_item_id":"0d4e8bbf6665de497184bc0c9354e209","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"What is the largest integral value of 'k' for which the quadratic equation x2 - 5x + k = 0 will have two real and distinct roots?","stimulus":"","stimulus_html":null,"stem_html":"<p>What is the largest integral value of &#x27;k&#x27; for which the quadratic equation x2 - 5x + k = 0 will have two real and distinct roots?</p>","rationale_html":"<p>Any quadratic equation will have real and distinct roots if the discriminant D &gt; 0</p><p>The discriminant &#x27;D&#x27; of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac</p><p>In this question, the value of D = 52 - 4 * 1 * k</p><p>If D &gt; 0, then 25 &gt; 4k or k &lt; 6.2.</p><p>Therefore, the highest integral value that k can take is 3.</p><p>correct choice is (C)</p>","correct_answer":["C"],"equiv_key":"39d8ed6ae8674bb05f5b6034","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>9</p>","ord":0},{"label":"B","content_html":"<p>7</p>","ord":1},{"label":"C","content_html":"<p>3</p>","ord":2},{"label":"D","content_html":"<p>8</p>","ord":3},{"label":"E","content_html":"<p>12</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}