Introduction - Quadratic Equation Video Lecture - Class 10

hello friends this video on quadratic
equations part one is brought to you by
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what we will study we will study
introduction quadratic equations
solution of quadratic equation by a
factorization solution of a quadratic
equation by completing the square nature
of roots and someone first
what is quadratic luciene quadratic
equation is nothing but a equation in
the form of ax square plus BX plus C is
equal to zero this form of equation is
called quadratic equation in variable X
why because you have used variable X X
is the variable and a B and C are real
numbers
they are constants and a should not be
equal to zero
let me repeat once again quadratic
equation in the variable X is nothing
but equation of the form ax square plus
BX plus C is equal to 0 where a b c are
real numbers and a should not be equal
to 0 because if is equal to 0 this
component is gone right then the
equation will be of a or form bx plus c
but the highest power if you see of in
that case c is 0 then the equation will
be bx plus c and in this the highest
power is 1 so it is no longer quadratic
equation this is a linear equation
quadratic equation as we have learned
that equation where the highest power is
2 here if you see the highest power of X
is 2
thus quadratic equation of the variable
X is nothing but equation of the form ax
square plus BX plus C where a B C are
real numbers and a should not be equal
to 0 let me take some example for
example 3 X square plus 2x plus 5 is
equal to 0 this is example of quadratic
equation why because this is of the form
ax squared plus BX plus C where a is
equal to 3 B is equal to 2 and C is
equal to 5 and E where a is not equal to
0
if I say 2x square plus 5 or 2 X square
plus 3 is equal to 0 this is also called
equation because this is a a is 2 B is 0
and C is 3 but if I make a is equal to 0
for example if I say 2x plus 3 is equal
to 0 because here a is 0 then this is
not a quiet equation because the rules
say that you should not be equal to 0 if
both B and C are 0 that is also if
example if I say X square is equal to 4
this is also or X square is going to 0
this is also a quadratic equation why
because here a component is not 0 is 1
correct so quadratic mission is nothing
but a form of equation of the form ax
square plus BX plus C is equal to 0
where a should not be equal to 0 and all
a B and C are real numbers they are
constant now now we have listed what is
quite education before going further
let's try to understand why do we really
need to read quadratic equation if you
don't learn chord equation what will
happen is it magnitude to learn word
equation let's do that if you see this
is the scenario where you have been told
that there is a rectangular lon I mean
normally do you have a rectangular lawn
near your house and you are told that
the length is twice the breadth if the
breadth is X let's suppose the length is
twice the bread that is 2 X and you have
been told the area is constant let's
suppose area is 30 to 32 meter square
and now you are asked to find the length
and width very very common sin anyway
when you have a lawn nearby and you have
been told that the area of the lawn is X
some some unit 32 meter square and you
have been told that length and breadth
has some relationship you have to find
the length and breadth how many do we
can do using quadratic machine example
here you say area is nothing but area of
lawn is nothing but length into breadth
is nothing but
l is equal to my to X and n is equal to
X that is to X square and we are also
telling that area is 32 meter square so
we can say that 2x squared is going to
32 meter square or we can see that X
square is equal to 16 if you see that
this is nothing but X square minus 16 is
equal to this is a quadratic equation
where a is 1 B is 0 and C is -16 current
and now we can solve this I will explain
you how to solve this in the next slides
but just try to understand this is one
real scenario where you may need quiet
equations the second scenario is the
projectile if you see in projectile it
suppose you're throwing a ball from here
to here you need beat once again you're
throwing a ball from here to here now
from here you have thrown the ball to
this one you want to find how much
distance it's covered you want to find
the distance s there suppose the
distance is s and you want to find the
distance as covered hard to find then
you use a physics formula in physics the
formula is s is equal to UT plus half ay
T Square if you don't understand the
formula leave it because you will learn
this in the higher classes just
understand this is a formula with which
you can find in distance where you will
constantly the initial velocity in
acceleration is also constant that is
actuation till it suppose you was a 5
and a was 6 let's suppose this is un
decently this is given so you can say
that this is nothing but 5d plus half
into 60 square cancel this is 3 that is
nothing but 5t + 3 d square if you see
that this is of the form of quietiy
equation correct because we can say that
5 DS t + 3 is going this is from quat
equation so here also if you want to
find the distance will use coordination
they are various scenarios in a real
life where we do use quiet equation in
terms of physics we extensively use
quiet equation in terms of aerodynamics
we use for at equations lot of places in
terms of finding the area's all the
architect use quiet equation so called
equation has
implementation it is very crucial for us
to understand Coweta confusion so let's
now try to understand let us try to
clear our concept empowered equation
thank you
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