<\/a>\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 2.3<\/span>\u00a0<\/strong><\/p>\nEx 2.3 Class 10 \u0917\u0923\u093f\u0924 Q1. \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0915\u0947, \u0928\u093f\u092e\u094d\u0928 \u092e\u0947\u0902 p(x) \u0915\u094b g(x) \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0928\u0947 \u092a\u0930 \u092d\u093e\u0917\u092b\u0932 \u0924\u0925\u093e \u0936\u0947\u0937\u092b\u0932 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f :<\/strong><\/p>\n(i) p(x) = x3<\/sup>\u00a0\u2013 3x2<\/sup>\u00a0+ 5x \u2013 3, g(x) = x2<\/sup>\u00a0\u2013 2<\/strong><\/p>\n(ii) p(x) = x4<\/sup>\u00a0\u2013 3x2<\/sup>\u00a0+ 4x + 5, g(x) = x2<\/sup>\u00a0+ 1 \u2013 x<\/strong><\/p>\n(iii) p(x) = x4<\/sup>\u00a0\u2013 5x + 6, g(x) = 2 \u2013 x2<\/sup><\/strong><\/p>\n\u0939\u0932 :<\/strong>\u00a0(i) p(x) = x3<\/sup>\u00a0\u2013 3x2<\/sup>\u00a0+ 5x \u2013 3, g(x) = x2<\/sup>\u00a0\u2013 2<\/strong><\/p>\n<\/p>\n
\u092d\u093e\u0917\u092b\u0932 q(x) = x – 3 \u0914\u0930 \u0936\u0947\u0937\u092b\u0932 = 7x – 9 \u0939\u0948 |<\/p>\n
\u0939\u0932 :<\/strong>\u00a0(ii) p(x) = x4<\/sup>\u00a0\u2013 3x2<\/sup>\u00a0+ 4x + 5, g(x) = x2<\/sup>\u00a0+ 1 \u2013 x<\/strong><\/p>\n<\/p>\n
\u092d\u093e\u0917\u092b\u0932 q(x) = x2<\/sup>\u00a0+ x – 3 \u0914\u0930 \u0936\u0947\u0937\u092b\u0932 = 8 \u0939\u0948 |<\/p>\n\u0939\u0932 :<\/strong>\u00a0(iii) p(x) = x4<\/sup>\u00a0\u2013 5x + 6, g(x) = 2 \u2013 x2<\/sup><\/strong><\/p>\n<\/p>\n
\u092d\u093e\u0917\u092b\u0932 q(x) = – x2<\/sup>\u00a0– 2 \u0914\u0930 \u0936\u0947\u0937\u092b\u0932 = – 5x + 10 \u00a0\u0939\u0948 |<\/p>\nEx 2.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q2. \u092a\u0939\u0932\u0947 \u092c\u0939\u0941\u092a\u0926 \u0938\u0947 \u0926\u0941\u0938\u0930\u0947 \u092c\u0939\u0941\u092a\u0926 \u0915\u094b \u092d\u093e\u0917 \u0915\u0930\u0915\u0947, \u091c\u093e\u0901\u091a \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0915\u094d\u092f\u093e \u092a\u094d\u0930\u0925\u092e \u092c\u0939\u0941\u092a\u0926 \u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0915\u093e \u090f\u0915 \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0939\u0948 :<\/strong><\/p>\n(i) t2<\/sup>\u00a0\u2013 3, 2t4<\/sup>\u00a0+ 3t3<\/sup>\u00a0\u2013 2t2<\/sup>\u00a0\u2013 9t \u2013 12<\/strong><\/p>\n(ii) x2<\/sup>\u00a0+ 3x + 1, 3x4<\/sup>\u00a0+ 5x3<\/sup>\u00a0\u2013 7x2<\/sup>\u00a0+ 2x + 2<\/strong><\/p>\n(iii) x3<\/sup>\u00a0\u2013 3x + 1, x5<\/sup>\u00a0\u2013 4x3<\/sup>\u00a0+ x2<\/sup>\u00a0+ 3x + 1<\/strong><\/p>\n\u0939\u0932 :<\/strong>\u00a0(i) t2<\/sup>\u00a0\u2013 3, 2t4<\/sup>\u00a0+ 3t3<\/sup>\u00a0\u2013 2t2<\/sup>\u00a0\u2013 9t \u2013 12<\/strong><\/p>\n<\/p>\n
\u091a\u0942\u0901\u0915\u093f \u0936\u0947\u0937\u092b\u0932 r(x) = 0 \u0939\u0948 |<\/p>\n
\u0905\u0924: t2<\/sup>\u00a0\u2013 3, 2t4<\/sup>\u00a0+ 3t3<\/sup>\u00a0\u2013 2t2<\/sup>\u00a0\u2013 9t \u2013 12 \u0915\u093e \u090f\u0915 \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0939\u0948 |<\/p>\n\u0939\u0932 :<\/strong>\u00a0(ii) x2<\/sup>\u00a0+ 3x + 1, 3x4<\/sup>\u00a0+ 5x3<\/sup>\u00a0\u2013 7x2<\/sup>\u00a0+ 2x + 2<\/strong><\/p>\n<\/p>\n
\u091a\u0942\u0901\u0915\u093f \u0936\u0947\u0937\u092b\u0932 r(x) = 0 \u0939\u0948 |<\/p>\n
\u0905\u0924: x2<\/sup>\u00a0+ 3x + 1, 3x4<\/sup>\u00a0+ 5x3<\/sup>\u00a0\u2013 7x2<\/sup>\u00a0+ 2x + 2 \u0915\u093e \u090f\u0915 \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0939\u0948 |<\/p>\n\u0939\u0932 :<\/strong>\u00a0(iii) x3<\/sup>\u00a0\u2013 3x + 1, x5<\/sup>\u00a0\u2013 4x3<\/sup>\u00a0+ x2<\/sup>\u00a0+ 3x + 1<\/strong><\/p>\n<\/p>\n
\u091a\u0942\u0901\u0915\u093f \u0936\u0947\u0937\u092b\u0932 r(x) = 2 \u0939\u0948 |<\/p>\n
\u0905\u0924: x3<\/sup>\u00a0\u2013 3x + 1, x5<\/sup>\u00a0\u2013 4x3<\/sup>\u00a0+ x2<\/sup>\u00a0+ 3x + 1 \u0915\u093e \u090f\u0915 \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0928\u0939\u0940\u0902 \u0939\u0948 |<\/p>\n<\/p>\n
\u0939\u0932 :<\/strong><\/p>\n\u0926\u093f\u092f\u093e \u0939\u0948 : p(x) = 3x4<\/sup>\u00a0+ 6x3<\/sup>\u00a0– 2x2<\/sup>\u00a0– 10x – 5<\/p>\n<\/p>\n
\u0905\u092c 3x2<\/sup>\u00a0– 5 \u0938\u0947 3x4<\/sup>\u00a0+ 6x3<\/sup>\u00a0– 2x2<\/sup>\u00a0– 10x – 5 \u092e\u0947\u0902 \u092d\u093e\u0917 \u0926\u0947\u0928\u0947 \u092a\u0930<\/p>\n<\/p>\n
\u0905\u0924: p(x) = (3x2<\/sup>\u00a0– 5) (x2<\/sup>\u00a0+ 2x + 1)<\/p>\n\u0905\u092c, x2<\/sup>\u00a0+ 2x + 1 \u0915\u094b \u0917\u0941\u0923\u0928\u0916\u0902\u0921 \u0915\u0930 \u0936\u0941\u0928\u094d\u092f\u0915 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 –<\/p>\n<\/p>\n
Ex 2.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q4. \u092f\u0926\u093f x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ x + 2 \u0915\u094b \u090f\u0915 \u092c\u0939\u0941\u092a\u0926 g(x) \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0928\u0947 \u092a\u0930, \u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937\u092b\u0932 \u0915\u094d\u0930\u092e\u0936: x – 2 \u0914\u0930 – 2x + 4 \u0939\u0948\u0902 \u0924\u094b g(x) \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f \u0964<\/strong><\/p>\n\u0939\u0932 :<\/strong><\/p>\n\u0926\u093f\u092f\u093e \u0939\u0948 : \u092d\u093e\u091c\u094d\u092f p(x) = x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ x + 2<\/p>\n\u092d\u093e\u0917\u092b\u0932 q(x) = x – 2,<\/p>\n
\u0936\u0947\u0937\u092b\u0932 r(x) = – 2x + 4<\/p>\n
\u092d\u093e\u091c\u0915 g(x) = ?<\/p>\n
\u092d\u093e\u091c\u094d\u092f = \u092d\u093e\u091c\u0915 \u00d7 \u092d\u093e\u0917\u092b\u0932 + \u0936\u0947\u0937\u092b\u0932<\/p>\n
p(x) = g(x) \u00d7 q(x) + r(x)<\/p>\n
x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ x + 2 = g(x) (x – 2) + (- 2x + 4)<\/p>\nx3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ x + 2 + 2x – 4 = g(x) (x – 2)<\/p>\ng(x) (x – 2) = x3<\/sup>\u00a0– 3x2<\/sup>\u00a0+ 3x – 2<\/p>\n<\/p>\n
\u0905\u0924: \u092d\u093e\u091c\u0915 g(x) = x2<\/sup>\u00a0– x + 1 \u0939\u0948 |<\/p>\nEx 2.3 Class 10 \u0917\u0923\u093f\u0924\u00a0Q5. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 p(x), g(x), q(x) \u0914\u0930 r(x) \u0915\u0947 \u0910\u0938\u0947 \u0909\u0926\u093e\u0939\u0930\u0923 \u0926\u0940\u091c\u093f\u090f \u091c\u094b \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0924\u0947 \u0939\u094b\u0902 \u0924\u0925\u093e<\/strong><\/p>\n(i) \u0918\u093e\u0924 p(x) = \u0918\u093e\u0924 q(x) \u0939\u094b<\/strong><\/p>\n(ii) \u0918\u093e\u0924 q(x) = \u0918\u093e\u0924 r(x) \u0939\u094b<\/strong><\/p>\n(iii) \u0918\u093e\u0924 r(x) = 0 \u0939\u094b<\/strong><\/p>\n\u0939\u0932 :<\/strong><\/p>\n\u092f\u0941\u0915\u094d\u0932\u093f\u0921 \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u092e \u0938\u0947<\/p>\n
p(x) = g(x) \u00d7 q(x) + r(x) \u00a0\u091c\u0939\u093e\u0901 q(x) \u00b9 0 \u0939\u094b<\/p>\n
(i) \u0918\u093e\u0924 p(x) = \u0918\u093e\u0924 q(x) \u0939\u094b<\/strong><\/p>\n\u092d\u093e\u091c\u094d\u092f p(x) \u0914\u0930 \u092d\u093e\u0917\u092b\u0932 q(x) \u0915\u0940 \u0918\u093e\u0924 \u0938\u093e\u092e\u093e\u0928 \u0924\u092d\u0940 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u092c \u092d\u093e\u091c\u0915 g(x)\u0915\u0940 \u0918\u093e\u0924 0 \u0905\u0930\u094d\u0925\u093e\u0924 \u0915\u094b\u0908 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b |<\/p>\n
\u0909\u0926\u093e\u0939\u0930\u0923 : \u092e\u093e\u0928\u093e p(x) = 2x2<\/sup>\u00a0– 6x + 3<\/p>\n\u0914\u0930 \u092e\u093e\u0928\u093e g(x) = 2<\/p>\n
\u092d\u093e\u0917 \u0926\u0947\u0928\u0947 \u092a\u0930<\/p>\n
p(x) = 2x2<\/sup>\u00a0– 6x + 2 + 1<\/p>\n= 2(x2<\/sup>\u00a0– 3x + 1) + 1<\/p>\n\u0905\u092c \u00a02(x2<\/sup>\u00a0– 3x + 1) + 1 \u0915\u094b p(x) = g(x) \u00d7 q(x) + r(x) \u0938\u0947 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 :<\/p>\n\u0905\u0924: q(x) = x2<\/sup>\u00a0– 3x + 1 \u0914\u0930 r(x) = 1<\/p>\n\u0907\u0938\u0938\u0947 \u0918\u093e\u0924 p(x) = \u0918\u093e\u0924 q(x) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |<\/p>\n
(ii) \u0918\u093e\u0924 q(x) = \u0918\u093e\u0924 r(x) \u0939\u094b<\/strong><\/p>\n\u0939\u0932 :<\/strong>\u00a0\u092f\u0939 \u0938\u094d\u0925\u093f\u0924\u093f \u0924\u092c \u0906\u0924\u0940 \u0939\u0948 \u091c\u092c p(x) \u0914\u0930 g(x) \u0915\u093e \u0918\u093e\u0924 \u0938\u093e\u092e\u093e\u0928 \u0939\u094b \u091c\u0948\u0938\u0947 –<\/p>\n\u092e\u093e\u0928\u093e p(x) = 2x2<\/sup>\u00a0+ 6x + 7 \u0914\u0930 g(x) = x2<\/sup>\u00a0+ 3x + 2<\/p>\n\u092d\u093e\u0917 \u0926\u0947\u0928\u0947 \u092a\u0930 : q(x) = 2 \u0914\u0930 r(x) = 3<\/p>\n
\u0905\u0924: \u0918\u093e\u0924 q(x) = \u0918\u093e\u0924 r(x) \u0939\u0948 |<\/p>\n
(iii) \u0918\u093e\u0924 r(x) = 0 \u0939\u094b<\/strong><\/p>\n\u0939\u0932 :<\/strong>\u00a0r(x) = 0 \u0924\u092c \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c p(x), g(x) \u0938\u0947 \u092a\u0942\u0930\u094d\u0923\u0924: \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0939\u094b :<\/p>\n\u092e\u093e\u0928\u093e p(x) = x2<\/sup>\u00a0– 1 \u0914\u0930 g(x) = x + 1<\/p>\n\u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930<\/p>\n
q(x) = x – 1 \u0914\u0930 r(x) = 0 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 |<\/p>\n
<\/a>\u092a\u094d\u0930\u0936\u094d\u0928\u093e\u0935\u0932\u0940 2.4<\/span><\/strong><\/p>\nEx 2.4 Class 10 \u0917\u0923\u093f\u0924 <\/strong>\u092a\u094d\u0930. 1. \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0940\u091c\u093f\u090f \u0915\u093f \u0928\u093f\u092e\u094d\u0928 \u0924\u094d\u0930\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0926\u0940 \u0917\u0908 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0909\u0938\u0915\u0940 \u0936\u0942\u0928\u094d\u092f\u0915 \u0939\u0948\u0902\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 \u0936\u0942\u0928\u094d\u092f\u0915\u094b\u0902 \u0914\u0930 \u0917\u0941\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927\u094d \u0915\u094b \u092d\u0940 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0940\u091c\u093f\u090f:
\n(i) 2x3<\/sup> + x2<\/sup> – 5x + 2; \\(\\frac { 1 }{ 2 }\\), 1, -2;<\/strong>
\n(ii) x3<\/sup> – 4x2<\/sup> + 5x – 2; 2, 1, 1<\/strong>
\n
\n
\n
\n<\/p>\nEx 2.4 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930\u0966 2. \u090f\u0915 \u0924\u094d\u0930\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0940\u091c\u093f\u090f \u091c\u093f\u0938\u0915\u0947 \u0936\u0942\u0928\u094d\u092f\u0915\u094b\u0902 \u0915\u093e \u092f\u094b\u0917, \u0926\u094b \u0936\u0942\u0928\u094d\u092f\u0915\u094b\u0902 \u0915\u094b \u090f\u0915 \u0938\u093e\u0925 \u0932\u0947\u0915\u0930 \u0909\u0928\u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 \u0924\u0925\u093e \u0924\u0940\u0928\u094b\u0902 \u0936\u0942\u0928\u094d\u092f\u0915\u094b\u0902 \u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932 \u0915\u094d\u0930\u092e\u0936\u0903 2, -7, -14 \u0939\u094b\u0902\u0964<\/strong>
\n<\/p>\nEx 2.4 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930\u0966 3. \u092f\u0935\u093f \u092c\u0939\u0941\u092a\u0935 x3<\/sup> – 3x2<\/sup> + x + 1 \u0915\u0947 \u0936\u0942\u0928\u094d\u092f\u0915 a – b, a, a + b \u0939\u094b\u0902, \u0924\u094b a \u0914\u0930 b \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong>
\n<\/p>\nEx 2.4 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930\u0966 4. \u092f\u0926\u093f \u092c\u0939\u0941\u092a\u0926 x4<\/sup> – 6x3<\/sup> – 26x2<\/sup> + 138x – 35 \u0915\u0947 \u0926\u094b \u0936\u0942\u0928\u094d\u092f\u0915 2 \u00b1 \u221a3 \u0939\u094b\u0902, \u0924\u094b \u0905\u0928\u094d\u092f \u0936\u0942\u0928\u094d\u092f\u0915 \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong>
\n<\/p>\nEx 2.4 Class 10 \u0917\u0923\u093f\u0924\u00a0\u092a\u094d\u0930\u0966 5. \u092f\u0926\u093f \u092c\u0939\u0941\u092a\u0926 x4<\/sup> – 6x3<\/sup> + 16x2<\/sup> – 25x + 10 \u0915\u094b \u090f\u0915 \u0905\u0928\u094d\u092f \u092c\u0939\u0941\u092a\u0926 x2<\/sup> – 2x + k \u0938\u0947 \u092d\u093e\u0917 \u0926\u093f\u092f\u093e \u091c\u093e\u090f \u0914\u0930 \u0936\u0947\u0937\u092b\u0932 x + a \u0906\u0924\u093e \u0939\u094b, \u0924\u094b k \u0924\u0925\u093e a \u091c\u094d\u091e\u093e\u0924 \u0915\u0940\u091c\u093f\u090f\u0964<\/strong>