Examples(NCERT):Zeroes of a Polynomial Video Lecture - Class 9

hello friends this video on polynomials
part 8 is brought to you by exam fear
calm no more fear from exam let us talk
about zeros of linear polynomial see
linear polynomial as told you I can
write a general form as a X plus B it is
not equal to zero find a linear
polynomial zeros let's suppose PC C is
the zero of the polynomial then a AC
plus B will be equal to zero so C we can
do minus B by so this is the zeros of
the linear final and please note this is
the only one zero right so linear
polynomial will have only one zeros for
example if you take P X is equal to X
minus 5 so if you see P 5 is the only 5
is the only 0 for this polynomial if you
take P X is equal to X plus 2 P of minus
2 is the only 0 for this polynomial
right so a linear polynomial will have
only one 0 let's see one example we have
to verify where 2 and 0 are 0 for this
point see this is not a linear
polynomial the highest power is 2 so
quadratic polynomial for a linear
polynomial the maximum number of 0 is 1
for quadratic the maximum of 0 is 2 and
let's see if 2 and 0 are zeros for this
polynomial so let's 0 square minus 2
into 0 and that is 0 minus 0 that is 0
so 0 is the 0 for this polynomial let us
talk about 2 so let's find the value of
P 2
so X becomes 2 2 square minus 2 X that
is 2 into 2 that is 4 minus 4 that is 0
so both 0 & 2 are 0 for this polynomial
please note linear polynomial will have
only one 0 quadratic can have at the max
to 0 and QB can have at the max 3 0 so
we observe that the 0 of the polynomial
need not be 0 0 of the polynomial can be
4 5 6 example x minus 5 0 of this
polynomial is Phi we also observe that 0
may be a zero of the polynomial for
example x square minus 2 X or this p 0
is also 0 so 0 may and may not be 0 the
other point of it every linear
polynomial has one and only one zero a
polynomial can have more than one zero
so this polynomial I'm talking about is
quadratic and cubic polynomial let's
take a few more numericals we need to
find the value of polynomial this at X
is equal to 0 X equal to minus 1 X is
going to pretty easy right so if my px
is given that is 5 X minus 4 X square
plus 3 I have to find p 0 to just
replace X with 0 right this is 0 this is
0 you get 3 it will replace X with minus
1 let us put P of minus 1 5 into X
become 5 into minus 1 minus 4 X square
is minus 1 square plus 3 that is nothing
but minus 5 minus 4 plus 3 minus 9 plus
3 that is minus 6 it's fine X equal to 2
P of 2 5 X becomes 5 into 2 minus 4 X
square becomes 4 into 2 square plus 3
just all this 5 into 2 is 10 2 square is
4 4 into 4 is 16 plus 3 that is 13
- 16 and that is nothing but minus three
and there is answer okay so we have to
find p0 p1 p2 for each of these let's do
four one for this let me find p0 I'll
put all Y is 0 V 2 square minus 0 plus 1
and that is 1 to find p1 let put all Y
as 1 1 square minus 1 plus 1 that is 1
let me find p2 all Y is 2 2 square minus
2 plus 1 that is 4 4 minus 2 plus 1 that
is 5 minus 2 that is 3 this is all for
this equation similarly you can do for
all this remaining 3 a Laden speed easy
just you have to put the run example
here all t is 0 then all TS 1 then all
TS so we have to check whether the
following it are the zeroes for this
point I will example you have to check
whether minus 1 by 3 s is 0 for this
point I mean 3x plus 1 so let's do that
will be replace - replace X with minus 1
by 3 the 3 eggs become 3 into minus 1 by
3 plus 1 that is minus 1 plus 1 that is
0 the next one px is equal to X square
minus 1 for 1 and minus 1 let's find for
p1 is 1 square is 1 that is 0 correct
it's fine 4 minus 1 that is X square is
minus 1 square minus 1 that is 1 minus 1
that is 0 yes for both of these actually
these numbers are 0 for these point of X
let's take this P X Square + X square to
0 so P of 0 is what 0 Square and that is
0 that means for this also it is true
let's take this so P of minus 1 by root
3 or this equation will be 3 into X
square that is minus 1 by root 3 minus 1
that is 3 into 1 by
3 minus 1 there is 1 minus 1 that is 0
let us take the value of p2 by root 3
now become 3 into X square that is 2 by
3 square minus 1 this becomes 3 into 4
by 3 minus 1 that is 4 minus 3 that is o
minus 1 that is 3 so for this it is true
but for this no okay let's take few more
numericals we had to find the zeros for
polynomials in each of these case first
is px is equal to X plus 5 so we have to
find some PC where this is equal 0 so
put xh c c plus 5 is equal to 0 C is
equal to minus 5 so for a first
polynomial my zeroes is minus 5 let's
take this one
similar px equal to X minus 5 so we have
to find a PC where PC is equal to 0
replace X with C C minus 5 is equal to 0
or C is equal to 5 this is also a zero
for this binomial let's try a six-month
x is not equal to 0 so this will be P of
0 is 0 2 your 0 is a into 0 so 0 is a 0
for this polynomial similarly you can do
rest of the cushions let me try this one
PX is going to CX plus D so let's let's
have a P I can use a different term
because he's already there I'll use P I
so CI plus D I is equal to D by C minus
device this is 0 right so what minus D
by C is the 0 for this part okay
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