{"id":679285,"date":"2023-09-03T02:58:29","date_gmt":"2023-09-02T21:28:29","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/find-a-quadratic-polynomial-whose-zeroes-are-5-3%e2%88%9a2-and-53%e2%88%9a2\/"},"modified":"2025-06-20T13:28:08","modified_gmt":"2025-06-20T07:58:08","slug":"find-a-quadratic-polynomial-whose-zeroes-are-5-3%e2%88%9a2-and-53%e2%88%9a2","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/find-a-quadratic-polynomial-whose-zeroes-are-5-32-and-532\/","title":{"rendered":"Find a quadratic polynomial whose zeroes are 5-3\u221a2 and 5+3\u221a2."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Find a quadratic polynomial whose zeroes are 5-3\u221a2 and 5+3\u221a2.","custom_permalink":"question\/mathematics\/find-a-quadratic-polynomial-whose-zeroes-are-5-32-and-532\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:0pt; line-height:normal; font-size:12pt\"><span><span>Find a quadratic polynomial whose zeroes are 5-3\u221a2 and 5+3\u221a2.<\/span><\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\"><spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><p><\/p><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\"><spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><p><\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\">","options":[{"option":"P(x)=<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">x<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span><span>\u221210x+7<\/span><\/span>","correct":true},{"option":"P(x)=<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">x<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span><span>\u221210x+5<\/span><\/span>","correct":false},{"option":"P(x)=<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">x<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span><span>\u221250x+7<\/span><\/span>","correct":false},{"option":"P(x)=<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">x<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span><span>\u221210x-7<\/span><\/span><span>&nbsp;<\/span>","correct":false}],"solution":"<span><span>Given that zeros of a polynomial are 5-3\u221a2 and 5+3\u221a2.<\/span><\/span><br><span>Now, polynomial is given by,<\/span><br><span>P(x)=<\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">x<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span>-(Sum of zeroes)x+ product of zeroes\u2026\u2026\u2026.(1)<\/span><br><span><span>Sum=(5\u22123\u221a2)+(5+3\u221a2)<\/span><\/span><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u21d2<\/mo><\/math><span>Sum=10<\/span><br><span><span>Product =(5\u22123\u221a2)(5+3\u221a2)<\/span><\/span><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo mathcolor=\"000000\">\u21d2<\/mo><mi mathcolor=\"000000\">Product<\/mi><mo mathcolor=\"000000\">=<\/mo><msup><mrow><mn mathcolor=\"000000\">5<\/mn><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><mo mathcolor=\"000000\">-<\/mo><msup><mrow><mfenced separators=\"|\"><mrow><mn mathcolor=\"000000\">3<\/mn><msqrt><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msqrt><\/mrow><\/mfenced><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><span>[<\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">a<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><mo mathcolor=\"000000\">-<\/mo><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">b<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><mo mathcolor=\"000000\">=<\/mo><mfenced separators=\"|\"><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">a<\/mi><mo mathcolor=\"000000\">-<\/mo><mi mathvariant=\"normal\" mathcolor=\"000000\">b<\/mi><\/mrow><\/mfenced><mfenced separators=\"|\"><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">a<\/mi><mo mathcolor=\"000000\">+<\/mo><mi mathvariant=\"normal\" mathcolor=\"000000\">b<\/mi><\/mrow><\/mfenced><\/math><span>]<\/span><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo mathcolor=\"000000\">\u21d2<\/mo><mi mathcolor=\"000000\">Product<\/mi><mo mathcolor=\"000000\">=<\/mo><mn mathcolor=\"000000\">25<\/mn><mo mathcolor=\"000000\">-<\/mo><mn mathcolor=\"000000\">9<\/mn><mo mathcolor=\"000000\">\u00d7<\/mo><mn mathcolor=\"000000\">2<\/mn><mi mathvariant=\"normal\" mathcolor=\"000000\">&nbsp;<\/mi><\/math><span> <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo mathcolor=\"000000\">\u21d2<\/mo><mi mathcolor=\"000000\">Product<\/mi><mo mathcolor=\"000000\">=<\/mo><mn mathcolor=\"000000\">25<\/mn><mo mathcolor=\"000000\">-<\/mo><mn mathcolor=\"000000\">18<\/mn><\/math><span> <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo mathcolor=\"000000\">\u21d2<\/mo><mi mathcolor=\"000000\">Product<\/mi><mo mathcolor=\"000000\">=<\/mo><mn mathcolor=\"000000\">7<\/mn><\/math><span> <\/span><span>From equation (1) we get,<\/span><br><span>P(x)=<\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">x<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span><span>\u221210x+7<\/span><\/span><br><span>Thus, the quadratic equation is P(x)=<\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mrow><mi mathvariant=\"normal\" mathcolor=\"000000\">x<\/mi><\/mrow><mrow><mn mathcolor=\"000000\">2<\/mn><\/mrow><\/msup><\/math><span><span>\u221210x+7 .<\/span><\/span><br><span>Therefore, option (1) is correct.<\/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>Find a quadratic 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