{"id":3611,"date":"2026-03-21T01:56:40","date_gmt":"2026-03-21T01:56:40","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3611"},"modified":"2026-04-19T11:19:04","modified_gmt":"2026-04-19T11:19:04","slug":"quadratic-equations","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/quadratic-equations\/","title":{"rendered":"\u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u2013 \u0930\u0902\u0917-\u0915\u094b\u0921\u093f\u0924 \u0917\u0923\u093f\u0924"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_ed88986f39805c81-238\" data-path-to-node=\"64\"><span data-path-to-node=\"64,0\"><b data-path-to-node=\"64,0\" data-index-in-node=\"0\">\u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/b> <\/span><span data-path-to-node=\"64,2\"><span class=\"citation-948\">\u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u093e (<\/span><span class=\"math-inline\" data-math=\"ax^2 + bx + c = 0\" data-index-in-node=\"30\">$ax^2 + bx + c = 0$<\/span><span class=\"citation-948\">\u0915\u093f\u0938\u0940 \u0935\u0938\u094d\u0924\u0941, \u091c\u0948\u0938\u0947 \u0917\u0947\u0902\u0926 \u092f\u093e \u0930\u0949\u0915\u0947\u091f, \u0915\u0947 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a \u092a\u0925 \u0915\u094b \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f (\u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948)<\/span><\/span><span data-path-to-node=\"64,4\">. <\/span><span data-path-to-node=\"64,6\"><span class=\"citation-947\">\u092f\u0939 \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0905\u091c\u094d\u091e\u093e\u0924 \u091a\u0930 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"64,8\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-239\" data-path-to-node=\"65\"><span data-path-to-node=\"65,0\"><b data-path-to-node=\"65,0\" data-index-in-node=\"0\">\u0915\u0939\u093e\u0928\u0940<\/b> <\/span><span data-path-to-node=\"65,2\"><span class=\"citation-946\">\u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u094d\u0915\u0942\u0932\u0940 \u092c\u091a\u094d\u091a\u0947 \u0915\u0947 \u0932\u093f\u090f \u201cX\u201d \u0915\u093e \u092e\u093e\u0928 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u093e \u090f\u0915 \u0906\u092e \u091a\u0941\u0928\u094c\u0924\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u092a\u094d\u0930\u093e\u091a\u0940\u0928 \u0915\u093e\u0932 \u092e\u0947\u0902 \u092f\u0939 \u0909\u0921\u093c\u0924\u0947 \u0939\u0941\u090f \u0924\u0940\u0930 \u0915\u0947 \u092a\u0925 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0940 \u0915\u0941\u0902\u091c\u0940 \u0925\u0940\u0964<\/span><\/span><span data-path-to-node=\"65,4\">. <\/span><span data-path-to-node=\"65,6\"><span class=\"citation-945\">\u091c\u092c \u092f\u0942\u0928\u093e\u0928\u0940 \u0907\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0906\u0915\u0943\u0924\u093f\u092f\u093e\u0901 \u092c\u0928\u093e\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930 \u0930\u0939\u0947 \u0925\u0947, \u0924\u092c \u092d\u093e\u0930\u0924\u0940\u092f \u0917\u0941\u0930\u0941 \u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0928\u0947 \u0935\u093f\u0936\u0941\u0926\u094d\u0927 \u0924\u0930\u094d\u0915 \u0915\u093e \u0938\u0939\u093e\u0930\u093e \u0932\u0947\u0928\u0947 \u0915\u093e \u0928\u093f\u0930\u094d\u0923\u092f \u0932\u093f\u092f\u093e\u0964<\/span><\/span><span data-path-to-node=\"65,8\">. <\/span><span data-path-to-node=\"65,10\"><span class=\"citation-944\">628 \u0908\u0938\u094d\u0935\u0940 \u092e\u0947\u0902, \u0935\u0947 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u094d\u092a\u0937\u094d\u091f \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0938\u092e\u093e\u0927\u093e\u0928 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u0939\u0932\u0947 \u0935\u094d\u092f\u0915\u094d\u0924\u093f \u092c\u0928\u0947\u0964<\/span><\/span><span data-path-to-node=\"65,12\">. <\/span><span data-path-to-node=\"65,14\"><span class=\"citation-943\">\u0909\u0928\u094d\u0939\u0947\u0902 &quot;\u0905\u0926\u0943\u0936\u094d\u092f&quot; \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092f\u093e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u092e\u0942\u0932\u094b\u0902 \u0938\u0947 \u0921\u0930 \u0928\u0939\u0940\u0902 \u0932\u0917\u0924\u093e \u0925\u093e\u2014\u092f\u0947 \u0910\u0938\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0901 \u0925\u0940\u0902 \u091c\u093f\u0928\u0938\u0947 \u0938\u0926\u093f\u092f\u094b\u0902 \u0924\u0915 \u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0917\u0923\u093f\u0924\u091c\u094d\u091e \u092d\u092f\u092d\u0940\u0924 \u0930\u0939\u0947 \u0925\u0947\u0964<\/span><\/span><span data-path-to-node=\"65,16\">. <\/span><span data-path-to-node=\"65,18\"><span class=\"citation-942\">\u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0930\u0902\u0917\u094b\u0902 \u0915\u093e \u092d\u0940 \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u093f\u092f\u093e, \u0905\u092a\u0928\u0947 \u091a\u0930\u094b\u0902 \u0915\u094b \u0915\u093e\u0932\u093e (\u0915\u0932\u0915\u093e) \u092f\u093e \u0928\u0940\u0932\u093e (\u0928\u0940\u0932\u093e) \u0928\u093e\u092e \u0926\u093f\u092f\u093e, \u091c\u093f\u0938\u0938\u0947 \u0926\u0941\u0928\u093f\u092f\u093e \u0915\u0940 \u092a\u0939\u0932\u0940 &quot;\u0930\u0902\u0917-\u0915\u094b\u0921\u093f\u0924&quot; \u0917\u0923\u093f\u0924\u0940\u092f \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0939\u0941\u0906\u0964<\/span><\/span><span data-path-to-node=\"65,20\">.<\/span><\/p>\n<p data-path-to-node=\"66\"><b data-path-to-node=\"66\" data-index-in-node=\"0\">\u0938\u092e\u092f\u0930\u0947\u0916\u093e<\/b><\/p>\n<table data-path-to-node=\"67\">\n<thead>\n<tr>\n<td><strong>\u092e\u0940\u0932 \u0915\u093e \u092a\u0924\u094d\u0925\u0930<\/strong><\/td>\n<td><strong>\u0935\u093f\u0935\u0930\u0923<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"67,1,0,0\"><b data-path-to-node=\"67,1,0,0\" data-index-in-node=\"0\">\u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0938\u0902\u0926\u0930\u094d\u092d.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-240\" data-path-to-node=\"67,1,1,0\"><span data-path-to-node=\"67,1,1,0,1\"><span class=\"citation-941\">1600 \u0908\u0938\u094d\u0935\u0940 (\u092f\u0942\u0930\u094b\u092a \u092e\u0947\u0902 \u092e\u093e\u0928\u0915\u0940\u0915\u0943\u0924) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"67,2,0,0\"><b data-path-to-node=\"67,2,0,0\" data-index-in-node=\"0\">\u092d\u093e\u0930\u0924\u0940\u092f \u0938\u094d\u0930\u094b\u0924<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-241\" data-path-to-node=\"67,2,1,0\"><span data-path-to-node=\"67,2,1,0,1\"><span class=\"citation-940\">628 \u0908. (\u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0915\u093e \u092c\u094d\u0930\u0939\u094d\u092e\u0938\u094d\u092b\u0941\u091f\u0938\u093f\u0926\u094d\u0927\u093e\u0928\u094d\u0924) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"67,3,0,0\"><b data-path-to-node=\"67,3,0,0\" data-index-in-node=\"0\">\u0936\u094d\u0932\u094b\u0915 \u0938\u0902\u0926\u0930\u094d\u092d<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-242\" data-path-to-node=\"67,3,1,0\"><span data-path-to-node=\"67,3,1,0,1\"><span class=\"citation-939\">\u092c\u094d\u0930\u0939\u094d\u092e\u0938\u094d\u092b\u0941\u091f\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 (18.44) (\u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u0928\u093f\u092f\u092e \u0926\u0947\u0924\u093e \u0939\u0948) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"67,4,0,0\"><b data-path-to-node=\"67,4,0,0\" data-index-in-node=\"0\">\u0915\u093e\u0932 \u0905\u0902\u0924\u0930\u093e\u0932<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-243\" data-path-to-node=\"67,4,1,0\"><span data-path-to-node=\"67,4,1,0,1\"><span class=\"citation-938\">900 \u0935\u0930\u094d\u0937\u094b\u0902 \u0938\u0947 \u0905\u0927\u093f\u0915 <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"p-rc_ed88986f39805c81-244\" data-path-to-node=\"68\"><span data-path-to-node=\"68,0\"><b data-path-to-node=\"68,0\" data-index-in-node=\"0\">\u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u0935\u093e\u091a\u093e\u0930<\/b> <\/span><span data-path-to-node=\"68,2\"><span class=\"citation-937\">\u092c\u094d\u0930\u0939\u094d\u092e\u0917\u0941\u092a\u094d\u0924 \u0928\u0947 \u092f\u0939 \u091c\u094d\u091e\u093e\u0924 \u0915\u093f\u092f\u093e \u0915\u093f \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0926\u094b \u0935\u0948\u0927 \u0939\u0932 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902: \u090f\u0915 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0914\u0930 \u090f\u0915 \u090b\u0923\u093e\u0924\u094d\u092e\u0915\u0964<\/span><\/span><span data-path-to-node=\"68,4\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-245\" data-path-to-node=\"69\"><span data-path-to-node=\"69,0\"><b data-path-to-node=\"69,0\" data-index-in-node=\"0\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0930\u093e\u0938\u0924<\/b> <\/span><span data-path-to-node=\"69,2\"><span class=\"citation-936\">\u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u091c\u094d\u091e\u093e\u0928 \u0915\u0940 \u0928\u0940\u0902\u0935 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"69,4\">. <\/span><span data-path-to-node=\"69,6\"><span class=\"citation-935\">\u0907\u0928\u0915\u0940 \u092e\u0926\u0926 \u0938\u0947 \u0939\u092e \u0917\u0924\u093f, \u0915\u094d\u0937\u0947\u0924\u094d\u0930\u092b\u0932 \u0914\u0930 \u092a\u094d\u0930\u0915\u094d\u0937\u0947\u092a\u094d\u092f \u0917\u0924\u093f \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930 \u0938\u0915\u0947\u0964<\/span><\/span><span data-path-to-node=\"69,8\">.<\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3503,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[579,544,577,578,580,576],"class_list":["post-3611","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-algebra","tag-ancient-indian-mathematics","tag-brahmagupta","tag-brahmasphutasiddhanta","tag-mathematical-logic","tag-quadratic-equations"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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