{"id":32260,"date":"2025-06-22T12:02:55","date_gmt":"2025-06-22T12:02:55","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=32260"},"modified":"2025-06-22T12:02:56","modified_gmt":"2025-06-22T12:02:56","slug":"when-solving-x2-3x-18-0-using-the-quadratic-formula-what-is-under-the-radical","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/when-solving-x2-3x-18-0-using-the-quadratic-formula-what-is-under-the-radical\/","title":{"rendered":"When solving x^2 &#8211; 3x &#8211; 18 = 0 using the quadratic formula, what is under the radical"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">When solving x^2 &#8211; 3x &#8211; 18 = 0 using the quadratic formula, what is under the radical?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Correct Answer: 81<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve the quadratic equation x2\u22123x\u221218=0x^2 &#8211; 3x &#8211; 18 = 0 using the quadratic formula, we first recall the formula: x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this equation, the coefficients are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=1a = 1<\/li>\n\n\n\n<li>b=\u22123b = -3<\/li>\n\n\n\n<li>c=\u221218c = -18<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The expression under the radical is called the <strong>discriminant<\/strong>, and it is represented by: b2\u22124acb^2 &#8211; 4ac<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute the values of aa, bb, and cc: (\u22123)2\u22124(1)(\u221218)(-3)^2 &#8211; 4(1)(-18)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">First, square \u22123-3: 9\u22124(1)(\u221218)9 &#8211; 4(1)(-18)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, calculate 4\u00d71\u00d7\u221218=\u2212724 \\times 1 \\times -18 = -72. So: 9\u2212(\u221272)=9+72=819 &#8211; (-72) = 9 + 72 = 81<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the value under the radical (the discriminant) is <strong>81<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The discriminant tells us about the nature of the solutions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the discriminant is positive and a perfect square (like 81), the equation has two real and rational solutions.<\/li>\n\n\n\n<li>If the discriminant is positive but not a perfect square, the equation has two real but irrational solutions.<\/li>\n\n\n\n<li>If it is zero, the equation has one real and repeated root.<\/li>\n\n\n\n<li>If it is negative, the solutions are complex (non-real).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Since 81 is a positive perfect square, we expect two real and rational roots.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To summarize, the value under the radical in the quadratic formula for the equation x2\u22123x\u221218=0x^2 &#8211; 3x &#8211; 18 = 0 is <strong>81<\/strong>, and it helps determine the type of roots the equation has.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When solving x^2 &#8211; 3x &#8211; 18 = 0 using the quadratic formula, what is under the radical? The correct answer and explanation is: Correct Answer: 81 To solve the quadratic equation x2\u22123x\u221218=0x^2 &#8211; 3x &#8211; 18 = 0 using the quadratic formula, we first recall the formula: x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a} [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-32260","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32260","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=32260"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32260\/revisions"}],"predecessor-version":[{"id":32265,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32260\/revisions\/32265"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=32260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=32260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=32260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}