00:00Welcome to RNNCAD.
00:02I am a RNNCAD.
00:03Today we are going to study class 10CBC.
00:07Chapter number 2.
00:09Which is Polynomials.
00:11Mathematics is the second chapter.
00:14But it is easy.
00:16So let's go.
00:19So let's go.
00:20So let's go.
00:20Let's go.
00:22So let's go.
00:24So let's go.
00:26So just let's talk.
00:31So you can start.
00:33Ollie is a mathematical expression.
00:36So what we need to know is that.
00:38It is a mathematical expression.
00:39The x which means x to c.
00:43This is a form.
00:44We can represent this.
00:46Our quadratic equation.
00:48Which means quadratic.
00:49objective
00:51Jadi
00:52definitely
00:53becaped
00:54and
00:57we can
00:58To
01:012x x square is a polynomial
01:042x x cube is a polynomial
01:052x x cube is a polynomial
01:09This is different
01:09This is different
01:12We can divide it in two types
01:151 to power and number of dumb
01:48is
01:49If you want to see which term is
01:51If you want to see which term is
01:532x
01:53So this single term is considered
01:57And if
01:592 plus x is
02:002 term
02:01So this term is
02:04constant term
02:05And this term
02:10Variable
02:18Variable
02:19But this term is
02:23Let's move on
02:23Now
02:24Now
02:25Now
02:28Now
02:29Now
02:30Now
02:31x square plus bx plus c equate
02:35में zero रखते हैं
02:36तो इसे quadratic equation कहेंगे
02:44ठीक, अब हम आगे चनते हैं
02:47इसमें जैसे लीखना भी आप पढ़ सकते हैं
02:49कि आप polynomialism mathematical expression
02:51हमने भी जाना
02:52constants होते हैं
02:54constants इसमें c term होते हैं
02:55या निवरिकल जिसकी value fixed हो
02:59fixed value हो
03:02fixed value
03:06variables इसकी value नहीं fixed हो
03:09no fixed value
03:15वो number हो आपको आपके बता ही है
03:17वो number exponents
03:19उसके बाद आते हैं हम इसको
03:21in में addition यूज़ कर सकता है
03:24subtraction यूज़ कर सकता है
03:25multiplication बैसे कि 2 इंटू 3
03:276 यह सब आते कहे रहे हैं
03:302 इंटू 3 x is equal to 6 x
03:34same चीज़ हम यूज़ कर सकते हैं
03:37अब इसमें rules भी होते हैं
03:38कई बार हम से क्यों में पूर लेता है
03:40इनमें सा कौन सा
03:42इस polynomial नहीं है
03:43और polynomial के जो variable होते हैं
03:47तुमकी पावर पहले बार तो अंडर रूट में नहीं हो सकती है
03:50जैसे कि देखे लिखा है यह अंडर रूट में नहीं हो सकती है
03:54यह होल नंबर होना वंबर सरी है
03:56यह है
03:58अब पढ़िए इसमें लिखा है कि रूल exponents must be non-negative इंडिज है
04:02exponents याने जो पावर रूट यहां पर exponent 3 है
04:07तो यह non-negative माने इसको positive होना है
04:10यह 0 से 1,2,3 से लेके infinite positive तक जा सकता है
04:16बढ़ negative नहीं होगा
04:18ठीक
04:20और आपको जैसे कि पता भी होगा एक exponents का रूल होता है
04:25यह simple अभी आप बात भी पढ़ेंगे
04:26अभी इन पर दादा यूज़ेंगे
04:29ठीक अब हम आगे जोते है variables
04:31इनकी value fixed ना हो
04:33x, y, z कुछ भी आप ले सकते हैं
04:36x, y, z ले ले ले इसको alpha ले ले, alpha कहते हैं
04:39beta ले ले, kapa ले, कुछ भी
04:42कुछ भी
04:44coefficient
04:45coefficient मने इसमें
04:47यह single term है
04:49और single term में
04:51तो आप देख सकते हैं
04:53numerical है, एक variable है
04:55तो three का coefficient मने उसके बगल वाला
04:58x
04:59जो x है, वो coefficient के लाएगा
05:08ठीक
05:09number of term के
05:11polynomial
05:13यह एक term है
05:14अगर plus, minus sign आएगा तब वो different term होगी नहींए
05:18इसलिकल कंसिडर की जाती है
05:20polynomial जिसमें
05:21दो term हो, जैसे देखे
05:23अभी मैंने बताया भी
05:24इसमें plus की current दो term होगी
05:26इसको single term ही consider किया जाएगा
05:29यह चीज़ को, अगर plus लग गया है
05:31अगर के बाद ही वो two term
05:33प्राइगा लागे
05:35तीन term
05:37अब डिग्री
05:38क्या होता है, वाइने यहां पर जो पावर होते है
05:41two, three जो भी लिखें देखते है
05:42quadratic की degree क्या होती है
05:45two
05:46cubic की degree क्या होती है
05:48three
05:50तो आपका मिजर लीज में
05:52quadratic तक क्यूबिक तो नहीं आता है
05:54पर फिर में आप देख नहीं थे
05:56क्योंकि हो questions पूछ लेते हैं कभी-कभी
05:58आपको पता होना चाहिए
06:00road learning नहीं होनी चाहिए
06:01understanding होनी चाहिए
06:04सब देखते हैं कि यह linear क्या है
06:06देखेंगे इसमें आपको x की power देखने है
06:08ना कि 1 की
06:10तो x की power यहां पर क्या है
06:12अगर जहां कुछ भी नहीं हो तो वहां बनाता है
06:14यहां x की power 1 है
06:16इसके बाद हम जलते हैं
06:18second में
06:20इसमें देखें x की जो highest power को calculate करते है
06:23highest power
06:25highest power
06:29क्योंकि आप देख सकते हैं
06:30आपर 8x भी है
06:32मायने यह linear भी है
06:33फिर भी इसको immediate क्यों नहीं कर कह रहे
06:36क्योंकि यह 3x वाद नाम भी है
06:37जिसकी power highest है
06:39ठीक
06:40तो इसको हम
06:43इसका graph जैसा आपने बता होगा
06:45यह
06:47यह graph होनता है यह x axis होती है
06:51यह y axis
06:55तो इसको एकर extend कर लेंगे
06:57तो इधर negative हो जाता है
06:59negative x और इधर extend कर लेंगे
07:02तो यह negative y
07:03तो यह
07:051, 2, 3
07:08minus 1, minus 2
07:09ऐसे ही जाएगा
07:10यह 1, 2, minus 1
07:13minus 2
07:14तो इसका graph समझ के
07:17यह understanding के लिए बताना था
07:19तो इसको लंबा से जिरियस कर थे
07:21नहीं तो समझ लिए है
07:22अच्छे से
07:27तो अब
07:27इसका straight value
07:28जो linear graph होता है
07:30मंदब बन जिसकी degree बन होती है
07:32उसका graph कुछ
07:34ऐसे बनता है
07:35straight line
07:38और
07:40इसको फिर एक बना नहीं देता है
08:00हो पर ऐसे भी बन सकता है
08:02आथसे यसे यू बन सकता है
08:03वो स्टों केश्पे बन करता है
08:05कि A positive है
08:08ए नेगटीव है
08:10वी कैसा है positive या
08:12negative या नेगटीव नेगटीव इस पर इपन करता है
08:15यज़
08:16आप आगे दें कुछे
08:18oh
08:19oh
08:20oh
08:22oh
08:25degree of the matter
08:29so
08:30highest exponent
08:35exponent
08:35exponent
08:37oh
08:37oh
08:38oh
08:40oh
08:40oh
08:41oh
08:41oh
08:42oh
08:42oh
08:43oh
08:43oh
08:43oh
08:43oh
08:43oh
08:43oh
08:43oh
08:44oh
08:47oh
08:56oh
09:02oh
09:02oh
09:02oh
09:02oh
09:03oh
09:03oh
09:07oh
09:07it is
09:08a
09:08graph
09:08to
09:09it
09:37sure
09:37now we have to do this
09:39linear graph
09:41linear equation
09:43x minus 5
09:46small to 0
09:47this graph
09:50straight
09:51we have to see
09:53x
09:55simple
09:58rx
09:59x
10:00x
10:00x
10:02x
10:02x
10:03x
10:03x
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10:16x
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10:31x
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10:37x
10:38x
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12:10x
12:10x
12:37x
12:38,
12:38,
12:38.
12:39.
12:39.
12:40.
12:41.
12:41.
12:41.
12:43Now we can see how we can get the solutions
12:46So, what is zero?
12:51Zero to root
12:54If we go deep, it's not a problem
12:58But we can't understand
13:00So
13:01I have equationism
13:03bx
13:04equation
13:04here
13:06bx
13:06x
13:06x
13:06x
13:07x
13:07x
13:07minus 4 so I'm a member x key as a very substitute can be
13:12a
13:12jokie poor question was 0 so I'm a school equal to me 0 substitute
13:17per game
13:18for
13:19right hand side
13:20is it
13:22okay
13:23I'm a school is going to be there is quite a
13:26right there is a
13:26right there is a
13:31right there is a
13:32right there is a
13:32right there is a
13:33do
13:35yes
13:37minus
13:38I
13:38minus
13:39minus
13:45solution
13:47solution
13:49minus
13:50minus
13:51minus
14:20minus
14:22Now, we substitute x value 2
14:25Now, we have 2 satisfied, 2-1 root
14:29If we have minus 2 satisfied, we have satisfied
14:32If we have minus 2 satisfied, we have satisfied
14:32Now, we have to do this graph
14:44So, we have graph
14:55foreign
14:59foreign
15:03foreign
15:05but this is y-axis
15:06x-axis
15:09one time single
15:11dependent
15:12equation
15:16tangent
15:17touch
15:18we have circle chapter
15:20tangent
15:2190 degree
15:21touch
15:22touch
15:26two zeros
15:28usual
15:29two times
15:30cut
15:30cut
15:31cut
15:33two zeros
15:34two distance zeros
15:36if
15:37square
15:38perfect
15:39square
15:39then
15:41two
15:42zero
15:43same
15:45three
15:46zero
15:47three time
15:48cut
15:48cut
15:50sorry
15:511
15:522
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15:55why
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18:19alpha plus beta
18:20then what b minus a
18:23k is coming
18:24b kya hootah coefficient of x
18:27e kya hootah coefficient of x square
18:30eisay hi
18:31agar product karen alpha or beta
18:33karen woh c upon a
18:35a a jayga
18:37thik
18:39c upon a
18:40c kya hai constant hai
18:46a kya hai coefficient of
19:17x square hai
19:19and the difficult level
19:19you can invent
19:21a good level
19:23you can say
19:27most important
19:28yt
19:29you can solve
19:30this
19:33this
19:36example
19:37we can
19:38think
19:38and
19:46to
19:47to
19:51to
19:52to
19:52to
19:53to
19:53to
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