Mathematical Equation Representation - Chapter 4 - Quadratic Equations, Class 10, Mathematics Video Lecture - Class 10 | Best Video for Class 10

hello friends this video on quadratic
equations part 2 is brought to you by
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no more fear from exam before watching
this video please make sure that you
have watched part 1 let's take the
scenario we have to represent this
mathematically so the cushion says John
and jivin 'they have 45 mothers took
away this guy is John and this lady is
given D John and even we have 45 mothers
together so if I assume and let me read
the question first both of them lost my
marble each and the product of the
number of marbles they have now is 124
you would like to find how many marbles
they had to start so let's do one thing
let's assume that John had X mod
correctly if John had X marble then G
went ahead how many moments let us
suppose it his wife Hollis now the first
thing is say that John marbles even thei
marvelous 45 right this is the statement
so I can say that Y is equal to 45 minus
X so as you're writing by all right 45
minus X because it will be only one
variable correct it's easy to have
equations in one variable if you have
more variables you have to solve more so
if John is having X variable X marbles
given T is having 45 minus X novel that
is the starting now both of them lost
five marble H so if you subtract five
from this this is becomes X minus five
because John has lost five marble G&T
also lost five hours so this is nothing
145 minus X minus five correct the
survivor is in marble and from that five
marble they have lost that is both of
them lost five marble is fine now they
are saying the product of the maahes
they have now is 124 that is if you
multiply this number
the current number of Mama's with John
has with the current number of Mama's
with Joanne thei has you'll get 124 so
it will solve this X minus 5 is the one
with John has and 45 minus X minus 5 I
can write this as nothing but 40 minus X
correct 45 minus I is 40 so X minus 5
into 40 minus X this is nothing but 120
that is what the question says if you
solve it further you will get X into 40
is nothing but 4 TX correct then X into
minus X is nothing but minus X square
minus 5 into 4 T is minus 200 minus 5
into minus X plus 5 X and that is
nothing but 1 2009 square or do you get
this as minus X square plus 5 X plus 40
X plus 45 X right minus 200 and this
will come this side from minus 320 4 is
equal to 0 or the same thing I'll put
everything on the right side because
minus X square doesn't look good to me
that becomes X square minus 45 X plus 3
24 is equal to so what is this this is
nothing but the equation in the form of
X where X is nothing but this value that
is marble John had in beginning so if
you see this is also one practical
example of quadratic equation where we
have to yeah we are not asked to solve
this question vienes asked you saw to
represent this mathematically so if you
solve this quadrature you get the answer
of the marble John hand we will learn
how to solve this quadratic equation in
the next few slides but just to start
with we have learned how to represent
the real-life scenario in mathematical
term let me repeat once again the
question says John and jimothy together
had 45 marbles to start please John had
X
and g13 had 45 minus X mumble because
you add this you get 45 then the
question say - both lost five marbles
so after loosing John had X minus 5 and
jimothy had 40 minus X Mar ones also the
quotients a separate of the marble they
have is 124 there is X minus 5 into 40
minus X going to 124 and we solve this
we got this equation that is X square
minus 45 X plus 320 Pole is equal to 0
this is how we represent in this
real-life scenario in the mathematical
term and this is a quadratic which we
know why because this is of the form ax
squared plus BX plus C is equal to 0
where a is 1 B is minus 45 and C is plus
3 D for correct let us take one more
example this also we have to represent
mathematically the question says a
cottage industry produces a certain
number of toys in a day the cost of
production of each toys in Group E was
formed to be 55 minus the total number
of toys produced on that day on a
particular day the total cost of
production was 750 we would like to find
how many toys where all that so what
let's suppose we'll assume C the
question is find out the number of toys
produced and a correct so we'll assume
that number of toys would you use but on
that days B X number of toys produced is
X correct now since the number of toys
produces eggs now the cost is what the
cost of the production of toy is nothing
but 55 minus number of toys correct so
cost part I is nothing but 55 minus 6
this is what pushes the same the
question is saying a cottage industry
produces a certain number of toys inity
we assume that certain number to be X
and the question says the cost of
production of each toy is 55 minus X so
per toys 55
six right on a particular day that total
cost of production was 750 so if you see
total cost of production
if you is nothing but number of toys
produced number of boys who used
interval multiply this Y cost per toy
correct see if you have five toy for
each toy if you are charging ten to B's
total cost is what fifty rupees five
into ten similarly here the total cost
of production will be number of toys
would use into cost per toy so what will
- right here this is 750 is equal to
number of pi produces X and the cost per
- is 55 minus X all right so let's solve
this or 750 is equal to 55 X minus X
square all wilting XY this side I will
get X square minus 55 X plus 750 is
equal to 0 where X is nothing but X is
number of toys produced and this is also
a quadratic equation if you see why
because this is also of the form ax
square plus BX plus C where a is 1 B is
minus 55 and C is 750 and we can solve
this how to solve this we'll know later
but just try to understand is the real
life scenario where it says that the
industry produces certain number of toys
in a DA and the cost of production of
each toy was 55 minus the number of toys
for you so what we have done we have
assumed the number of toys produced was
X on that particular day so the cost per
day will be cost per toy will be 55
minus X so total cost is number of toys
produced into cost per day per toy that
is X into 5 minus X and that value is
750 already given in the question thank
you
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