{"id":10827,"date":"2022-05-31T13:43:13","date_gmt":"2022-05-31T08:13:13","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10827"},"modified":"2022-05-31T13:43:14","modified_gmt":"2022-05-31T08:13:14","slug":"if-the-polynomial-x4-6x3-16x2-25x-10-is-divided-by-another-polynomial-x2-2x-k-the-remainder-comes-out-to-x-a-find-x-and-a","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-the-polynomial-x4-6x3-16x2-25x-10-is-divided-by-another-polynomial-x2-2x-k-the-remainder-comes-out-to-x-a-find-x-and-a\/","title":{"rendered":"If the polynomial \\(x^4 – 6x^3 + 16x^2 – 25x + 10\\) is divided by another polynomial \\(x^2 – 2x + k\\), the remainder comes out to x + a, find x and a."},"content":{"rendered":"

Solution :<\/h2>\n

Let us divide \\(x^4 – 6x^3 + 16x^2 – 25x + 10\\) by \\(x^2 – 2x + k\\)<\/p>\n

\"polynomial<\/p>\n

\\(\\therefore\\)\u00a0 Remainder = (2k – 9)x – (8 – k)k + 10<\/p>\n

But the remainder is given as x + a,<\/p>\n

On comparing their coefficients, we have :<\/p>\n

2k – 9 = 1\u00a0 \\(\\implies\\)\u00a0 k = 5<\/p>\n

and -(8 – k)k + 10 = a<\/p>\n

So, a = -(8 – 5)5 + 10<\/p>\n

a = -15 + 10 = – 5<\/p>\n

Hence, k = 5 and a = -5<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let us divide \\(x^4 – 6x^3 + 16x^2 – 25x + 10\\) by \\(x^2 – 2x + k\\) \\(\\therefore\\)\u00a0 Remainder = (2k – 9)x – (8 – k)k + 10 But the remainder is given as x + a, On comparing their coefficients, we have : 2k – 9 = 1\u00a0 \\(\\implies\\)\u00a0 k …<\/p>\n

If the polynomial \\(x^4 – 6x^3 + 16x^2 – 25x + 10\\) is divided by another polynomial \\(x^2 – 2x + k\\), the remainder comes out to x + a, find x and a.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,910],"tags":[],"yoast_head":"\nIf the polynomial \\(x^4 - 6x^3 + 16x^2 - 25x + 10\\) is divided by another polynomial \\(x^2 - 2x + k\\), the remainder comes out to x + a, find x and a. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/if-the-polynomial-x4-6x3-16x2-25x-10-is-divided-by-another-polynomial-x2-2x-k-the-remainder-comes-out-to-x-a-find-x-and-a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the polynomial \\(x^4 - 6x^3 + 16x^2 - 25x + 10\\) is divided by another polynomial \\(x^2 - 2x + k\\), the remainder comes out to x + a, find x and a. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Let us divide (x^4 – 6x^3 + 16x^2 – 25x + 10) by (x^2 – 2x + k) (therefore)\u00a0 Remainder = (2k – 9)x – (8 – k)k + 10 But the remainder is given as x + a, On comparing their coefficients, we have : 2k – 9 = 1\u00a0 (implies)\u00a0 k … If the polynomial (x^4 – 6x^3 + 16x^2 – 25x + 10) is divided by another polynomial (x^2 – 2x + k), the remainder comes out to x + a, find x and a. 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