{"id":226689,"date":"2025-06-05T12:54:54","date_gmt":"2025-06-05T12:54:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226689"},"modified":"2025-06-05T12:54:56","modified_gmt":"2025-06-05T12:54:56","slug":"what-is-a-smart-birds-favorite-type-of-math","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/what-is-a-smart-birds-favorite-type-of-math\/","title":{"rendered":"What Is A Smart Bird&#8217;s Favorite Type of Math"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">What Is A Smart Bird&#8217;s Favorite Type of Math? To answer the question, use the values of a, b, and c of each of the following quadratic equations in determining the sum and product of their roots. Write the corresponding letter in the box matching the given sum and product. L x^2 + x = 6 B 12x^2 + x &#8211; 6 = 0 G x^2 &#8211; 2x &#8211; 2 = 0 R 2x^2 + 5x &#8211; 25 = 0 A 6x^2 &#8211; 5x &#8211; 4 = 0 O 3x^2 &#8211; 11x &#8211; 4 = 0 E 4x &#8211; 5 = -4x^2 W 8x^2 + 12x = -1 Answer Box answer sum of roots product of roots 11 3 -3 2 -1 2 -1 -1 12 -5 2 5 6 -4 3 1 8 -6 -2 -5 4 1 2 -25 2 -2 3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-158.png\" alt=\"\" class=\"wp-image-226690\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve this, we use the formulas for the sum and product of the roots of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sum of roots<\/strong> = \u2212ba-\\frac{b}{a}<\/li>\n\n\n\n<li><strong>Product of roots<\/strong> = ca\\frac{c}{a}<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s analyze each equation and match with the values from the answer box:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. L: x2+x=6\u21d2x2+x\u22126=0x^2 + x = 6 \\Rightarrow x^2 + x &#8211; 6 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=1,b=1,c=\u22126a = 1, b = 1, c = -6<\/li>\n\n\n\n<li>Sum = \u221211=\u22121-\\frac{1}{1} = -1, Product = \u221261=\u22126\\frac{-6}{1} = -6 \u2192 Match: <strong>(-1, -6)<\/strong> \u2192 Letter: <strong>L<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. B: 12&#215;2+x\u22126=012x^2 + x &#8211; 6 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=12,b=1,c=\u22126a = 12, b = 1, c = -6<\/li>\n\n\n\n<li>Sum = \u2212112-\\frac{1}{12}, Product = \u2212612=\u221212\\frac{-6}{12} = -\\frac{1}{2} \u2192 Match: <strong>(-1\/12, -1\/2)<\/strong> \u2192 Letter: <strong>B<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. G: x2\u22122x\u22122=0x^2 &#8211; 2x &#8211; 2 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=1,b=\u22122,c=\u22122a = 1, b = -2, c = -2<\/li>\n\n\n\n<li>Sum = \u2212\u221221=2-\\frac{-2}{1} = 2, Product = \u221221=\u22122\\frac{-2}{1} = -2 \u2192 Match: <strong>(2, -2)<\/strong> \u2192 Letter: <strong>G<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. R: 2&#215;2+5x\u221225=02x^2 + 5x &#8211; 25 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=2,b=5,c=\u221225a = 2, b = 5, c = -25<\/li>\n\n\n\n<li>Sum = \u221252-\\frac{5}{2}, Product = \u2212252\\frac{-25}{2} \u2192 Match: <strong>(-5\/2, -25\/2)<\/strong> \u2192 Letter: <strong>R<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5. A: 6&#215;2\u22125x\u22124=06x^2 &#8211; 5x &#8211; 4 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=6,b=\u22125,c=\u22124a = 6, b = -5, c = -4<\/li>\n\n\n\n<li>Sum = \u2212\u221256=56-\\frac{-5}{6} = \\frac{5}{6}, Product = \u221246=\u221223\\frac{-4}{6} = -\\frac{2}{3} \u2192 Match: <strong>(5\/6, -2\/3)<\/strong> \u2192 Letter: <strong>A<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>6. O: 3&#215;2\u221211x\u22124=03x^2 &#8211; 11x &#8211; 4 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=3,b=\u221211,c=\u22124a = 3, b = -11, c = -4<\/li>\n\n\n\n<li>Sum = \u2212\u2212113=113-\\frac{-11}{3} = \\frac{11}{3}, Product = \u221243=\u221243\\frac{-4}{3} = -\\frac{4}{3} \u2192 Match: <strong>(11\/3, -4\/3)<\/strong> \u2192 Letter: <strong>O<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>7. E: 4x\u22125=\u22124&#215;2\u21d24&#215;2+4x\u22125=04x &#8211; 5 = -4x^2 \\Rightarrow 4x^2 + 4x &#8211; 5 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=4,b=4,c=\u22125a = 4, b = 4, c = -5<\/li>\n\n\n\n<li>Sum = \u221244=\u22121-\\frac{4}{4} = -1, Product = \u221254\\frac{-5}{4} \u2192 Match: <strong>(-1, -5\/4)<\/strong> \u2192 Letter: <strong>E<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>8. W: 8&#215;2+12x+1=08x^2 + 12x + 1 = 0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=8,b=12,c=1a = 8, b = 12, c = 1<\/li>\n\n\n\n<li>Sum = \u2212128=\u221232-\\frac{12}{8} = -\\frac{3}{2}, Product = 18\\frac{1}{8} \u2192 Match: <strong>(-3\/2, 1\/8)<\/strong> \u2192 Letter: <strong>W<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Matching:<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Sum of Roots<\/th><th>Product of Roots<\/th><th>Letter<\/th><\/tr><\/thead><tbody><tr><td>11\/3<\/td><td>-4\/3<\/td><td>O<\/td><\/tr><tr><td>3\/2<\/td><td>1\/8<\/td><td>W<\/td><\/tr><tr><td>-1<\/td><td>-6<\/td><td>L<\/td><\/tr><tr><td>2<\/td><td>-2<\/td><td>G<\/td><\/tr><tr><td>-1<\/td><td>-5\/4<\/td><td>E<\/td><\/tr><tr><td>-1\/12<\/td><td>-1\/2<\/td><td>B<\/td><\/tr><tr><td>-5\/2<\/td><td>-25\/2<\/td><td>R<\/td><\/tr><tr><td>5\/6<\/td><td>-2\/3<\/td><td>A<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Riddle Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The correct letters spell: <strong>OWL-ALGEBRA<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Explanation (300 words):<\/strong><br>This activity asks us to determine the sum and product of the roots of given quadratic equations. Using the fundamental theorem of algebra, any quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0 has roots with:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sum = \u2212ba-\\frac{b}{a}<\/li>\n\n\n\n<li>Product = ca\\frac{c}{a}<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We apply this to each of the 8 equations, carefully simplifying fractions. Once we calculate each pair, we match them to the corresponding values in the answer box, which gives us a letter for each pair.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, in the equation x2+x=6x^2 + x = 6, we rewrite it as x2+x\u22126=0x^2 + x &#8211; 6 = 0, so a=1,b=1,c=\u22126a = 1, b = 1, c = -6. This gives a sum of roots of \u22121-1 and product of \u22126-6, matching a box that reveals the letter &#8220;L&#8221;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Repeating this process for each equation provides the full set of letters. Arranged in order of the answer box, these letters spell <strong>\u201cOWL ALGEBRA\u201d<\/strong>, which cleverly answers the riddle: <strong>\u201cWhat is a smart bird\u2019s favorite type of math?\u201d<\/strong>.<br>The answer is: <strong>OWL-gebra!<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-470.jpeg\" alt=\"\" class=\"wp-image-226691\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What Is A Smart Bird&#8217;s Favorite Type of Math? To answer the question, use the values of a, b, and c of each of the following quadratic equations in determining the sum and product of their roots. Write the corresponding letter in the box matching the given sum and product. L x^2 + x = [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-226689","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226689","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=226689"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226689\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}