{"id":17701,"date":"2026-05-02T19:13:41","date_gmt":"2026-05-02T13:13:41","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/nature-of-roots-for-parameter-8\/"},"modified":"2026-05-02T19:13:41","modified_gmt":"2026-05-02T13:13:41","slug":"nature-of-roots-for-parameter-8","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/nature-of-roots-for-parameter-8\/","title":{"rendered":"Nature Of Roots For Parameter -8"},"content":{"rendered":"<p>For the quadratic equation x^2 + (-10)x + -8 = 0, determine the nature of its roots.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>one rational and one irrational root<\/li>\n<li>two equal real roots<\/li>\n<li>two distinct real roots<\/li>\n<li>no real root<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705],"subject":[1425],"education_level":[1896],"class_list":["post-17701","mcq","type-mcq","status-publish","hentry","topic-algebra","subject-mathematics","education_level-hsc"],"mcq_note":"Think of this as a discriminant question. For a quadratic equation ax^2 + bx + c = 0, first identify a = 1, b = -10, and c = -8. Now calculate D = b^2 - 4ac = (-10)^2 - 4(1)(-8) = 132. Since D &gt; 0, the equation has two distinct real roots. Because it is positive but not a perfect square, the two real roots are irrational.","mcq_options":[{"right":"no","answer":"one rational and one irrational root"},{"right":"no","answer":"two equal real roots"},{"right":"yes","answer":"two distinct real roots"},{"right":"no","answer":"no real root"}],"multi_answers":"no","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/17701","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=17701"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=17701"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=17701"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=17701"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=17701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}