{"id":234203,"date":"2025-06-14T02:16:09","date_gmt":"2025-06-14T02:16:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234203"},"modified":"2025-06-14T02:16:11","modified_gmt":"2025-06-14T02:16:11","slug":"what-two-numbers-multiply-to-42-and-add-to-19","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/what-two-numbers-multiply-to-42-and-add-to-19\/","title":{"rendered":"what two numbers multiply to -42 and add to 19"},"content":{"rendered":"\n<p>what two numbers multiply to -42 and add to 19<\/p>\n\n\n\n<p><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<h6 class=\"wp-block-heading\">ChatGPT said:<\/h6>\n\n\n\n<p>To find two numbers that <strong>multiply to -42<\/strong> and <strong>add to 19<\/strong>, we begin by identifying the properties of the numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Their <strong>product<\/strong> is <strong>-42<\/strong>, which means one number is <strong>positive<\/strong> and the other is <strong>negative<\/strong> (because a negative times a positive gives a negative).<\/li>\n\n\n\n<li>Their <strong>sum<\/strong> is <strong>positive 19<\/strong>, which means the <strong>positive number is greater in magnitude<\/strong> than the negative one.<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s find all factor pairs of -42:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(-1, 42) \u2192 -1 + 42 = 41<\/li>\n\n\n\n<li>(-2, 21) \u2192 -2 + 21 = 19 \u2714<\/li>\n\n\n\n<li>(-3, 14) \u2192 -3 + 14 = 11<\/li>\n\n\n\n<li>(-6, 7) \u2192 -6 + 7 = 1<\/li>\n\n\n\n<li>(1, -42) \u2192 1 + (-42) = -41<\/li>\n\n\n\n<li>(2, -21) \u2192 2 + (-21) = -19<\/li>\n\n\n\n<li>(3, -14) \u2192 3 + (-14) = -11<\/li>\n\n\n\n<li>(6, -7) \u2192 6 + (-7) = -1<\/li>\n<\/ul>\n\n\n\n<p>Among these, the pair <strong>(-2, 21)<\/strong> satisfies both conditions:<br><strong>-2 \u00d7 21 = -42<\/strong> and <strong>-2 + 21 = 19<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Textbook-Style Explanation<\/h3>\n\n\n\n<p>When solving a problem that asks for two numbers based on their product and sum, it helps to follow a structured approach. Begin by identifying the <strong>target product<\/strong> and the <strong>target sum<\/strong>. In this case, we are looking for two numbers whose <strong>product is -42<\/strong> and <strong>sum is 19<\/strong>.<\/p>\n\n\n\n<p>Since the product is <strong>negative<\/strong>, it indicates that one number is <strong>positive<\/strong> and the other is <strong>negative<\/strong>. A positive number multiplied by a negative number always yields a negative result. The fact that their sum is <strong>positive<\/strong> suggests that the <strong>positive number must be larger in magnitude<\/strong> than the negative one.<\/p>\n\n\n\n<p>Next, list all the factor pairs of 42. These pairs are combinations of numbers that multiply to 42. Then, assign a negative sign to one number in each pair to explore possible combinations whose product is -42. Check each pair to see if their <strong>sum equals 19<\/strong>.<\/p>\n\n\n\n<p>When we test the pair <strong>(-2, 21)<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The product is <strong>-2 \u00d7 21 = -42<\/strong><\/li>\n\n\n\n<li>The sum is <strong>-2 + 21 = 19<\/strong><\/li>\n<\/ul>\n\n\n\n<p>This pair satisfies both conditions. Therefore, the two numbers we are looking for are <strong>-2 and 21<\/strong>.<\/p>\n\n\n\n<p>This method of factoring is commonly used in algebra, especially when solving quadratic equations of the form <em>ax\u00b2 + bx + c = 0<\/em>, where identifying such pairs helps factor the trinomial into simpler expressions.<\/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-banner5-493.jpeg\" alt=\"\" class=\"wp-image-234204\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>what two numbers multiply to -42 and add to 19 The Correct Answer and Explanation is: ChatGPT said: To find two numbers that multiply to -42 and add to 19, we begin by identifying the properties of the numbers: Let\u2019s find all factor pairs of -42: Among these, the pair (-2, 21) satisfies both conditions:-2 [&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 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