{"id":648762,"date":"2023-06-27T01:28:46","date_gmt":"2023-06-26T19:58:46","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/how-many-polynomials-can-be-formed-by-using-5-and-3-as-zeroes\/"},"modified":"2025-06-26T13:11:14","modified_gmt":"2025-06-26T07:41:14","slug":"how-many-polynomials-can-be-formed-by-using-5-and-3-as-zeroes","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/how-many-polynomials-can-be-formed-by-using-5-and--3-as-zero\/","title":{"rendered":"How many polynomials can be formed by using 5 and -3 as zeroes?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"How many polynomials can be formed by using 5 and -3 as zeroes?","custom_permalink":"question\/mathematics\/how-many-polynomials-can-be-formed-by-using-5-and--3-as-zero\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:0pt; line-height:normal\"><span>How many polynomials can be formed by using 5 and -3 as zeroes?<\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><spanstyle=\"-aw-import:ignore\"><p><\/p><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><spanstyle=\"-aw-import:ignore\"><p><\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":[{"option":"<span>1<\/span>","correct":false},{"option":"<span>0<\/span>","correct":false},{"option":"<span>2<\/span>","correct":false},{"option":"<span>infinite<\/span><span>&nbsp;<\/span>","correct":true}],"solution":"<span>We have to find the number of polynomials that have their zeroes as 5 and -3.<\/span><br><span>The general form of a quadratic polynomial is, <\/span><img src=\"data:image\/jpeg;base64,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\" width=\"357\" height=\"24\" alt=\"\" class=\"image_resized\" style=\"width:357px;height:24px\"><span>where <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mi>\u03b1<\/m:mi>\r\n <\/m:semantics><\/math>&nbsp;<span> and <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mi>\u03b2<\/m:mi>\r\n <\/m:semantics><\/math>&nbsp;<span> are the zeroes of the polynomial. <\/span><br><span>Since, the zeroes of the polynomial as 5 and -3, then,<\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mtable columnalign=\"left\" equalrows=\"true\" equalcolumns=\"true\">\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mi>\u03b1<\/m:mi><m:mo>=<\/m:mo><m:mn>5<\/m:mn><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mi>\u03b2<\/m:mi><m:mo>=<\/m:mo><m:mo>\u2212<\/m:mo><m:mn>3<\/m:mn><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    \r\n   <\/m:mtable><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<br><span>By using the above values we get, <\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:msup>\r\n    <m:mi>x<\/m:mi>\r\n    <m:mn>2<\/m:mn>\r\n   <\/m:msup>\r\n   <m:mo>\u2212<\/m:mo><m:mn>2<\/m:mn><m:mi>x<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>15<\/m:mn><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span> <\/span><span>However, because it equals zero, we can multiply it with a constant without changing the value, i.e.,<\/span><br><span>&nbsp;<\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mi>k<\/m:mi><m:mfenced close=\"]\" open=\"[\">\r\n    <m:mrow>\r\n     <m:msup>\r\n      <m:mi>x<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msup>\r\n     <m:mo>\u2212<\/m:mo><m:mn>3<\/m:mn><m:mi>x<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>10<\/m:mn><\/m:mrow>\r\n   <\/m:mfenced><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>. <\/span><br><span>where k is an infinitely variable constant.<\/span><br><span>As a result, the number of polynomials is also infinite.<\/span><br><span>Thus, there are an infinite number of polynomials with the numbers 5 and -3.<\/span><br><span>Hence, option 4 is the correct option.<\/span><br><span>&nbsp;<\/span>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How many polynomials can be formed by using 5 and -3 as zeroes? - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"How many polynomials can be formed by using 5 and -3 as zeroes?\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/how-many-polynomials-can-be-formed-by-using-5-and--3-as-zero\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta 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