त्रिघाती बहुपद - Revision history

Ramamurthy at 15:22, 26 September 2024

2024-09-26T15:22:24Z

← Older revision		Revision as of 20:52, 26 September 2024
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	<math>x^3-23x^2+142x-120=(x-1)(x-10)(x-12)</math>		<math>x^3-23x^2+142x-120=(x-1)(x-10)(x-12)</math>
	[[Category:बहुपद]][[Category:~~कक्षा-9~~]][[Category:~~गणित~~]]		[[Category:बहुपद]]
			[[Category:गणित]]
			[[Category:कक्षा-9]]

Mani at 05:26, 11 May 2024

2024-05-11T05:26:27Z

← Older revision		Revision as of 10:56, 11 May 2024
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	<math>x^2(x-1)-22x(x-1)+120(x-1)</math>		<math>x^2(x-1)-22x(x-1)+120(x-1)</math>

	<math>(x-1)(x^2-22x+120)</math> सर्वनिष्ठ ~~तथ्य~~ <math>(x-1)</math> लेने पर		<math>(x-1)(x^2-22x+120)</math> सर्वनिष्ठ गुणक <math>(x-1)</math> लेने पर

	अब, गुणनखंडन <math>x^2-22x+120</math> करने पर		अब, गुणनखंडन <math>x^2-22x+120</math> करने पर

Mani at 05:23, 11 May 2024

2024-05-11T05:23:58Z

← Older revision		Revision as of 10:53, 11 May 2024
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	<math>(x-10)(x-12)</math>		<math>(x-10)(x-12)</math>




	<math>x^3-23x^2+142x-120=(x-1)(x-10)(x-12)</math>		<math>x^3-23x^2+142x-120=(x-1)(x-10)(x-12)</math>

	[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]		[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]

Mani: content added

2024-05-11T05:23:19Z

content added

← Older revision		Revision as of 10:53, 11 May 2024
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	~~A cubic polynomial is a type of polynomial with the highest power of the variable or degree to be~~ <math>3</math>~~. Cubic polynomials are used in various areas of mathematics and science~~, ~~including physics, engineering, and economics.~~		त्रिघाती बहुपद एक प्रकार का बहुपद है जिसमें चर या घात की उच्चतम घात <math>3</math> होती है। त्रिघाती बहुपद का उपयोग भौतिकी, इंजीनियरिंग और अर्थशास्त्र सहित गणित और विज्ञान के विभिन्न क्षेत्रों में किया जाता है।

	== ~~Definition~~ ==		== परिभाषा ==
	~~A cubic polynomial is a polynomial with the highest exponent of a variable i.e. degree of a variable as~~ <math>3</math>~~. The general form of a cubic polynomial is~~ <math>ax^3+bx^2+cx+d=0</math>, ~~<math>a \ne 0</math>, where~~ <math>a,b,c</math> ~~are coefficients and~~ <math>d</math> ~~is the constant with all of them being real numbers. An equation involving a cubic polynomial is called a cubic equation.~~		त्रिघाती बहुपद, एक ऐसा बहुपद है जिसमें एक चर का उच्चतम घातांक होता है अर्थात चर का घात <math>3</math> होता है। एक त्रिघाती बहुपद का सामान्य रूप <math>ax^3+bx^2+cx+d=0</math> है, जहां <math>a,b,c</math> गुणांक हैं और <math>d</math> वह स्थिरांक है जिसमें वे सभी वास्तविक संख्या हैं।

	~~Some of the examples of a cubic polynomial are~~		त्रिघाती बहुपद वाले समीकरण को त्रिघाती समीकरण कहा जाता है।

			त्रिघाती बहुपद के कुछ उदाहरण इस प्रकार हैं

	<math>4x^3</math> , <math>2x^3+1</math> , <math>5x^3+x^2</math> , <math>2x^3+4x^2+6x+7</math>		<math>4x^3</math> , <math>2x^3+1</math> , <math>5x^3+x^2</math> , <math>2x^3+4x^2+6x+7</math>

	== ~~Example~~ ==		== उदाहरण ==
	~~Factorise~~ <math>x^3-23x^2+142x-120</math>		गुणनखंडन <math>x^3-23x^2+142x-120</math> करने पर

	<math>x^3-23x^2+142x-120</math>		<math>x^3-23x^2+142x-120</math>
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	<math>x^2(x-1)-22x(x-1)+120(x-1)</math>		<math>x^2(x-1)-22x(x-1)+120(x-1)</math>

	<math>(x-1)(x^2-22x+120)</math> ~~Taking~~ <math>(x-1)</math> ~~common~~		<math>(x-1)(x^2-22x+120)</math> सर्वनिष्ठ तथ्य <math>(x-1)</math> लेने पर

	~~Now factorise~~ <math>x^2-22x+120</math>		अब, गुणनखंडन <math>x^2-22x+120</math> करने पर

	<math>x^2-22x+120</math>		<math>x^2-22x+120</math>
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	<math>(x-10)(x-12)</math>		<math>(x-10)(x-12)</math>

Mani at 05:05, 11 May 2024

2024-05-11T05:05:31Z

← Older revision		Revision as of 10:35, 11 May 2024
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			A cubic polynomial is a type of polynomial with the highest power of the variable or degree to be <math>3</math>. Cubic polynomials are used in various areas of mathematics and science, including physics, engineering, and economics.

			== Definition ==
			A cubic polynomial is a polynomial with the highest exponent of a variable i.e. degree of a variable as <math>3</math>. The general form of a cubic polynomial is <math>ax^3+bx^2+cx+d=0</math>, <math>a \ne 0</math>, where <math>a,b,c</math> are coefficients and <math>d</math> is the constant with all of them being real numbers. An equation involving a cubic polynomial is called a cubic equation.

			Some of the examples of a cubic polynomial are

			<math>4x^3</math> , <math>2x^3+1</math> , <math>5x^3+x^2</math> , <math>2x^3+4x^2+6x+7</math>

			== Example ==
			Factorise <math>x^3-23x^2+142x-120</math>

			<math>x^3-23x^2+142x-120</math>

			<math>x^3-x^2-22x^2+22x+120x-120</math>

			<math>x^2(x-1)-22x(x-1)+120(x-1)</math>

			<math>(x-1)(x^2-22x+120)</math> Taking <math>(x-1)</math> common

			Now factorise <math>x^2-22x+120</math>

			<math>x^2-22x+120</math>

			<math>x^2-10x-12x+120</math>

			<math>x(x-10)-12(x-10)</math>

			<math>(x-10)(x-12)</math>



			<math>x^3-23x^2+142x-120=(x-1)(x-10)(x-12)</math>

	[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]		[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]
	~~Cubic Polynomial~~

Mani at 06:34, 16 August 2023

2023-08-16T06:34:15Z

← Older revision		Revision as of 12:04, 16 August 2023
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	[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]		[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]
			Cubic Polynomial

Ramamurthy: Category updated

2023-08-05T06:25:29Z

Category updated

← Older revision		Revision as of 11:55, 5 August 2023
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	~~[[Category:बीजगणित]]~~
	[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]		[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]

Sarika at 05:27, 4 August 2023

2023-08-04T05:27:29Z

← Older revision		Revision as of 10:57, 4 August 2023
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	[[Category:बीजगणित]]		[[Category:बीजगणित]]
	[[Category:बहुपद]][[Category:कक्षा-9]]		[[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]

Sarika at 05:20, 4 August 2023

2023-08-04T05:20:24Z

← Older revision		Revision as of 10:50, 4 August 2023
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	[[Category:बीजगणित]]		[[Category:बीजगणित]]
	[[Category:बहुपद]]		[[Category:बहुपद]][[Category:कक्षा-9]]

Sarika at 10:50, 18 April 2023

2023-04-18T10:50:37Z

← Older revision		Revision as of 16:20, 18 April 2023
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	~~[[Category:गणित]]~~
	[[Category:बीजगणित]]		[[Category:बीजगणित]]
	[[Category:बहुपद~~]][[Category: कक्षा -9~~]]		[[Category:बहुपद]]