Quadratic Equations Video Lecture | Mathematics (Maths) Class 10

0:0:0: did you know the word quadratic was
0:0:3: derived from a Latin word which means
0:0:5: Square so in algebra we use quadratic
0:0:9: equation to refer to any equation with
0:0:11: the highest power of two for
0:0:13: examples 2x² + 3 x 1 = 0 x² + 7 = 0 5 x²
0:0:24: equal to
0:0:25: 0 imagine you have a rectangle with area
0:0:29: equal to 300 M squ and sides equal to 2x
0:0:33: + 1 and X let's try to make an
0:0:36: expression out of it we all know the
0:0:39: formula to calculate the area of a
0:0:41: rectangle which is length multiplied by
0:0:44: breadth so here we get 2 x + 1 * X on
0:0:50: multiplying we get 2 x² + x also because
0:0:55: we know that the area is equal to 300 M
0:0:59: Square we can write WR 2x² + x = 300
0:1:4: m² what do you think is this a quadratic
0:1:8: equation let's
0:1:10: analyze first is this an
0:1:13: equation yes it is why because it has an
0:1:18: equal sign in it now what do you think
0:1:22: is it a quadratic
0:1:25: equation yes you are absolutely right it
0:1:29: is a quadratic
0:1:30: equation why as we studied a quadratic
0:1:34: equation has the highest power of a
0:1:36: variable equal to two now let's
0:1:40: generalize the quadratic equation if we
0:1:43: put a instead of 2 b instead of 1 and C
0:1:46: instead of 300 we get a x² + b x + C is
0:1:50: equal to 0 this is called the standard
0:1:54: form of a quadratic equation with a
0:1:57: condition that a cannot be equal to zero
0:2:1: why because if a becomes equal to zero
0:2:4: the term of x² will also disappear and
0:2:7: the basic definition of quadratic
0:2:9: equation that the equation has highest
0:2:11: power of to will not be
0:2:13: satisfied so always remember a quadratic
0:2:18: equation is always of the form a x² + b
0:2:21: x + C is equal to 0 where a is not equal
0:2:24: to zero let's now try some questions
0:2:27: from exercise
0:2:28: 4.1 the first question says check
0:2:32: whether the following are quadratic
0:2:35: equations x + 1 s = to 2 * x - 3 do you
0:2:42: think this is a quadratic equation does
0:2:45: it satisfy the condition let's try
0:2:49: together now here we need to always be
0:2:53: careful before judging anything the
0:2:55: first task should always be simplifying
0:2:58: the equation here we need to open up the
0:3:2: brackets x + 1 s isn't it similar to an
0:3:7: identity we have
0:3:8: studied which one is it yes it is A + B
0:3:13: squ which is equal to a² + b² + 2 a
0:3:19: similarly we open this bracket we get x²
0:3:23: + 1 s + 2 * x * 1 and on the right hand
0:3:28: side we have 2 * x - 3 opening this
0:3:33: bracket we get 2 x - 2 * 3 that is 6 so
0:3:39: equating LHS and rhs we get x² + 1 + 2x
0:3:44: = 2 x - 6 on solving this equation we
0:3:49: get x² + 7 = 0 here we can see that the
0:3:54: highest power of the variable X is 2 so
0:3:59: it is a quad quadratic
0:4:0: equation so while solving these types of
0:4:3: questions always remember to First
0:4:6: simplify the expression and then judge
0:4:8: whether it is a quadratic equation or
0:4:10: not let's move on to the next question
0:4:14: that is represent the following
0:4:16: situations in the form of quadratic
0:4:19: equations here's a tip to tackle these
0:4:21: type of questions always write down the
0:4:24: information as you read the
0:4:26: question let's start the a area of a
0:4:30: rectangular plot is 528 m squ so we note
0:4:35: down that the area of the rectangle is
0:4:37: equal to 528 m squar the length of the
0:4:42: plot in met is one more than twice its
0:4:45: breadth here if we take breadth to be X
0:4:49: therefore the length comes out to be 2x
0:4:52: + 1 we need to find the length and
0:4:55: breadth of the
0:4:56: plot so we have length equal 2x + 1 and
0:5:1: bread equal to X and area equal to 528
0:5:6: m² also we know the formula for area of
0:5:9: rectangle that is length into breadth =
0:5:12: 2x + 1 into x = 528
0:5:17: m² therefore the equation comes out to
0:5:20: be 2x² + x - 528 is equal to 0 and this
0:5:25: is indeed a quadratic equation do try
0:5:29: the rest of the questions on your
0:5:31: own now that we have understood how to
0:5:34: form a quadratic equation we will move
0:5:36: on to the next section which is solution
0:5:38: of a quadratic equation by
0:5:41: factorization consider a quadratic
0:5:43: equation 2x^2 - 3x + 1 = 0 if we replace
0:5:49: X by 1 on the left hand side we get 2
0:5:53: into 1 2 - 3 into 1 + 1 which turns out
0:5:56: to be 0er which is the right hand side
0:6:0: this implies one is a root of the
0:6:2: quadratic
0:6:3: equation so in general a real number
0:6:6: Alpha is called the root of a quadratic
0:6:8: equation only if it satisfies the
0:6:11: equation the method of factorization we
0:6:14: are going to study is called middle term
0:6:17: splitting let us consider the standard
0:6:19: form of quadratic equation that is ax² +
0:6:23: BX + c equal 0 in this method we have to
0:6:28: split the middle number which is B into
0:6:30: two numbers p and Q such that p + Q is
0:6:34: equal to B and P into Q is equal to a
0:6:37: multiplied by C let's try a question to
0:6:41: better understand the
0:6:42: concept find the roots of the quadratic
0:6:45: equation 6 x^2 - x - 2 = 0 so here if we
0:6:52: compare this quadratic equation with the
0:6:54: standard form a x² + b x + C = 0 we get
0:6:59: get = to 6 B = -1 and C = to
0:7:4: -2 so for splitting middle term method
0:7:7: we need to split minus1 in two numbers p
0:7:10: and Q such that p + Q = to min-1 and P
0:7:14: into Q = to a into C = 6 into -2 =
0:7:20: -12 think yourself P can be minus 4 and
0:7:24: Q can be 3 let's check once if these
0:7:28: values satisfy the
0:7:29: conditions p + Q = - 4 + 3 = to -1 and
0:7:35: it is indeed equal to B P into Q = -4
0:7:40: into 3 = -12 and this is equal to a into
0:7:44: C = to
0:7:46: -2 so we write 6 x 2 - 4x + 3x - 2 = 0
0:7:54: next step is to take out common
0:7:56: numbers so we take out 2 x X common from
0:8:0: the first two terms and one from the
0:8:2: last two terms we get 2x into 3x - 2 + 1
0:8:7: into 3x - 2 again we see 3x - 2 to be
0:8:13: common we take that also out and get 3x
0:8:17: - 2 * 2x + 1 so we get two values of X
0:8:23: by solving 3x - 2 and 2 x + 1 which are
0:8:27: -1 by 2 and 2 by 3 hence the roots of
0:8:32: the quadratic equation are -1x 2 and 2x
0:8:36: 3 we hope that you have understood the
0:8:38: concept of quadratic
0:8:40: equations now here's a secret on how you
0:8:43: can study effectively with the urv app
0:8:47: you can learn with chapter notes watch
0:8:49: video lectures and solve ncer based McQ
0:8:53: tests of this chapter on
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0:8:58: amazing courses for class 10 and much
0:9:0: more for your class 10
0:9:2: preparation thank you