L7 : Zeroes of polynomial - Polynomials, Maths, Class 9 Video Lecture - Class 9 | Best Video for Class 9

hello friends this video on polynomials
part 7 is brought to you by exam fear
calm no more fear from exam now I'll
talk about zeroes of polynomial C for
example anomia let's suppose P X is
equal to X minus 2 0 the polynomial is
nothing but the value of x at which this
polynomial becomes 0 you see X minus 2
is equal to 0 and that happens at X is
equal to 2 that means I can say that P
of 2 is nothing but 2 minus 2 that is 0
right so if P of X is X minus 2 P of 2
is 2 minus 2 replacing X with 2 and that
is C let's solve this equation in this
one p FX is less suppose X minus 2 let's
find a low P of 1 PF 1 will be what
replace X with 1 1 minus 2 that is minus
1
let's find P of 0 P of 0 will be what 0
minus 2 that is minus 2
let's find P of 2 P of 2 would be 1 2
minus 2 that is 0 so if you see here
this becomes 0 so zeros of the
polynomial is the number C for which 4px
they are PC 0 for example I have PX in
equation let's suppose X square plus 4 X
plus 4 right if there is a PC where this
whole thing is 0 so this number C is
called zeros so I will say here C is
zeros of x so where I can say that in
this equation 2 is the zeros of px their
px is X minus 2 C this is C 0 is very
important right so in the graph I mean
if you in the higher classes will you
know draw try to plot the graph for this
so the point at which term if the
equation is 0 that point is little
critical
is that typically those point to the
solution for those scraps Hey
so will not talk in detail about the
graph no it will you not understand but
this understand that whenever this whole
polynomial becomes zero
see this whole polynomial will become
zero for some value of x right so the
value of x ash which these polynomial
becomes zero that is called zero of this
polynomial example this polynomial will
become zero I think let's find the value
of P of minus 2 minus 2 square plus 4 of
minus 2 plus 4 this becomes 4 minus 8
plus 4 and it is 0 so if you see at
minus 2 this px becomes 0 so minus 2 is
the zero of this polynomial similarly 2
is the 0 of this point I mean if you
have another problem it suppose X minus
1 so this polynomial will become 0 at Z
is equal to 1 so 1 is the 0 of this
polynomial 2 is the 0 of this polynomial
minus 2 is the zero this polynomial
alright so if you have let's suppose P X
as X minus Phi so here if you talk about
P Phi will be nothing but Phi minus 5
that is 0 so here 5 is a zero of this
polynomial okay so there are some
polynomial for example px is equal to 8
let suppose so this will never have any
zero because for any value of x this
will not become 0 because there is no X
here right so in this kind of poem this
is a polynomial for information so this
kind of polynomial will never become 0
okay or let us suppose
P X is X square plus one right if we
talk about X has to be zero it will be
minus root 1 that would be match
renumber it for real number this will
also not have any zeros okay so you can
find some of the polynomial which will
not have 0 also we have some polynomial
which is always 0 for example if you
have px is equal to 0 zero point oval so
for any real number this is 0 so for
every real number every real number is 0
of this point will because you take P 1
P 2 P 3 V 4 or any real number this is
always 0
that's why 0 polynomial is little
different right so they are indefinite
number of zeros of a zero point or mill
that is 1 and in fact the degree of 0
polynomial is also not defined so please
note 0 polynomial and zeros of point
normal these are two different tough
this is example of 0 polynomial 0
polynomial is nothing but 0 zeros of
polynomial is nothing but point where I
mean the value of x where this whole
polynomial value is 0
let me repeat once again zero point I
mean is nothing but 0 px is equal to
zero this is zero point amel and zeros
of a polynomial is nothing but point
where this px becomes zero for example
at to this px becomes 0 at 1 this px X
minus 1 becomes 0 at minus 2 this px X
square plus 4x plus 4 becomes 0 at 5
this px that is X minus 5 becomes 0
right so that those are zeroes of the
polynomial okay so don't confuse with
zeroes of the polynomial n 0 polynomial
so we talked a lot about zeroes of point
what is special about this what is so
big deal about this we spend so much
time understanding zeros of the
polynomial actually there is something
special about it see for any P X P X if
PC is zero then I can say C is zero of P
I'm just writing the definition once
again if that is the case then X minus C
will be factor of P X this is a concert
will study later just introducing you
with the concept for example let's take
P X is X square minus 1 so let's find P
1 P 1 is 1 square minus 4 that is not
equal to 0 P 2 is 2 square minus 4 that
is equal to 0 so if you see P 2 is 0 the
polynomial that means I can say that X
minus 2 is factor of X square minus 1
just by finding the 0 of the polynomial
I can say that X minus that number the 0
of the polynomial is a factor of this
whole px X minus 0 of the polynomial is
the factor of P X thus the introduction
anyway we'll study about this in detail
in X few slides so let us take some
examples now we need to check whether -2
n 2 are zeros of this polynomial X plus
2 so I have px is equal to X plus 2 so I
have to check whether P minus 2 NP 2 is
0 or not P minus 2 is what replace X
with minus 2 and P 2 is what replace X
with 2 so in this case this is 0 in this
case it is not 0 it is 4 so I can say
that minus 2 is zeroes of P
but plus 2 is nonzero of px okay find
the zero of point ml 2x plus 1 so 4 0 px
is equal to 2x plus 1 so there is a
number C which is 0 of this polynomial
so what PC has to be 0 find the value of
C C becomes minus 1 by 2 so I can say
that P of minus 1 by 2 is equal to 0 I
can show you once again replace X with
minus 1 by 2 plus 1 that is nothing but
minus 1 plus 1 that is 0 so minus 1 by 2
is 0 of px equal to 2x plus 4 this
polynomial minus 1 by 2 is the 0 okay
thank you visit our website exam viacom
to watch more and more qualities we
should be news you can also attend free
online tests that are there in our
website you can also get access to tons
of free study materials and you can also
find free tutors and mentors in this
website thanks a lot for watching