{"id":679280,"date":"2023-09-03T02:57:31","date_gmt":"2023-09-02T21:27:31","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/if-the-sum-of-the-zeroes-of-the-quadratic-polynomial-3x2-kx6-is-3-then-find-the-value-of-k\/"},"modified":"2025-06-20T13:27:19","modified_gmt":"2025-06-20T07:57:19","slug":"if-the-sum-of-the-zeroes-of-the-quadratic-polynomial-3x2-kx6-is-3-then-find-the-value-of-k","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-the-sum-of-the-zeroes-of-the-quadratic-polynomial-3x2-kx\/","title":{"rendered":"If the sum of the zeroes of the quadratic polynomial 3×2-kx+6\u00a0is\u00a03, then find the value of k."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"If the sum of the zeroes of the quadratic polynomial 3x2-kx+6\u00a0is\u00a03, then find the value of k.","custom_permalink":"question\/mathematics\/if-the-sum-of-the-zeroes-of-the-quadratic-polynomial-3x2-kx\/"},"categories":[],"acf":{"question":"

If the sum of the zeroes of the quadratic polynomial <\/span>3<\/mn>x<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>-<\/mo>kx<\/mi>+<\/mo>6<\/mn> is <\/mi>3<\/mn><\/math>, then find the value of k.<\/span><\/p>

<\/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":"0<\/mn><\/math>","correct":false},{"option":"9<\/mn><\/math>","correct":true},{"option":"7<\/mn><\/math>","correct":false},{"option":"3<\/mn><\/math> <\/span>","correct":false}],"solution":"Given that, sum of zeros of <\/span>3<\/mn>x<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>-<\/mo>kx<\/mi>+<\/mo>6<\/mn> is <\/mi>3<\/mn><\/math>.<\/span>
The sum of roots are <\/span>-<\/mo>b<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac><\/math>.<\/span>
From given equation, comparing with <\/span>a<\/mi>x<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>+<\/mo>bx<\/mi>+<\/mo>c<\/mi>=<\/mo>0<\/mn>,<\/mo> <\/mi><\/math>we get,<\/span>
a<\/mi>=<\/mo>3<\/mn>,<\/mo> b<\/mi>=<\/mo>-<\/mo>k<\/mi><\/math>, <\/span>c<\/mi>=<\/mo>6<\/mn><\/math>  <\/span>So, the sum of roots = <\/span>-<\/mo>b<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>-<\/mo>b<\/mi><\/mrow>a<\/mi><\/mrow><\/mfrac>=<\/mo>-<\/mo>-<\/mo>k<\/mi><\/mrow><\/mfenced><\/mrow>3<\/mn><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>3<\/mn>=<\/mo>k<\/mi><\/mrow>3<\/mn><\/mrow><\/mfrac><\/math> <\/span>\u21d2<\/mo>k<\/mi>=<\/mo>9<\/mn><\/math> <\/span>Thus, if the sum of zeroes of the quadratic polynomial <\/span>3<\/mn>x<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>-<\/mo>kx<\/mi>+<\/mo>6<\/mn>=<\/mo>0<\/mn>  <\/mi><\/math>is <\/span>3<\/mn><\/math>, then the value of <\/span>k<\/mi>=<\/mo>9<\/mn>.<\/mo><\/math>
Therefore, option (2) is correct.<\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nIf the sum of the zeroes of the quadratic polynomial 3x2-kx+6\u00a0is\u00a03, then find the value of k. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"If the sum of the zeroes of the quadratic polynomial 3x2-kx+6\u00a0is\u00a03, then find the value of k.\" \/>\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\/if-the-sum-of-the-zeroes-of-the-quadratic-polynomial-3x2-kx\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the sum of the zeroes of the quadratic polynomial 3x2-kx+6\u00a0is\u00a03, then find the value of k. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"If the sum of the zeroes of the quadratic polynomial 3x2-kx+6\u00a0is\u00a03, then find the value of k.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-the-sum-of-the-zeroes-of-the-quadratic-polynomial-3x2-kx\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-20T07:57:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"If the sum of the zeroes of the quadratic polynomial 3x2-kx+6\u00a0is\u00a03, then find the value of k. - 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