{"id":17720,"date":"2026-05-02T19:15:58","date_gmt":"2026-05-02T13:15:58","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/root-expression-from-sum-and-product-4-21\/"},"modified":"2026-05-02T19:15:58","modified_gmt":"2026-05-02T13:15:58","slug":"root-expression-from-sum-and-product-4-21","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/root-expression-from-sum-and-product-4-21\/","title":{"rendered":"Root Expression From Sum And Product 4 -21"},"content":{"rendered":"<p>If \u03b1 and \u03b2 are roots of x^2 &#8211; (4)x + (-21) = 0, find \u03b1^2 + \u03b2^2.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>63<\/li>\n<li>-26<\/li>\n<li>433<\/li>\n<li>58<\/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-17720","mcq","type-mcq","status-publish","hentry","topic-algebra","subject-mathematics","education_level-hsc"],"mcq_note":"Use Vieta's formulas instead of solving the quadratic. For x^2 - (4)x + (-21) = 0, the roots \u03b1 and \u03b2 satisfy \u03b1 + \u03b2 = 4 and \u03b1\u03b2 = -21. The expression we need is \u03b1^2 + \u03b2^2. Use the identity \u03b1^2 + \u03b2^2 = (\u03b1 + \u03b2)^2 - 2\u03b1\u03b2. So \u03b1^2 + \u03b2^2 = (4)^2 - 2(-21) = 16 - (-42) = 58. This is why the correct answer is 58.","mcq_options":[{"right":"no","answer":"63"},{"right":"no","answer":"-26"},{"right":"no","answer":"433"},{"right":"yes","answer":"58"}],"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\/17720","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=17720"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=17720"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=17720"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=17720"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=17720"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}