verify whether x=-1/√3, 2/√3 are zeroes of polynomial p(x)=3x²-1
Answers
Answer:
In order to verify the values are zeros of polynomial p(x), we must replace the variable x with the given values.
If p(x)=0, then that given value is zero of polynomial p(x).
(i) p(x)=3x+1
Put x=−
3
1
, we get
p(x)=3(−
3
1
)+1=−1+1=0
So, x=−
3
1
is the zero of the polynomial p(x).
(ii) p(x)=5x−π
Put x=
5
4
, we get
p(x)=5(
5
4
)−π=4−π
=0
So, x=
5
4
is not the zero of the polynomial p(x).
(iii) p(x)=x
2
−1
Put x=1, we get
p(x)=(1)
2
−1=1−1=0
So, x=1 is the zero of the polynomial p(x).
p(x)=x
2
−1
Put x=−1, we get
p(x)=(−1)
2
−1=1−1=0
So, x=−1 is the zero of the polynomial p(x).
(iv) p(x)=(x+1)(x−2)
Put x=−1, we get
p(x)=(−1+1)(−1−2)=0(−3)=0
So, x=−1 is the zero of the polynomial p(x).
Put x=−2, we get
p(x)=(2+1)(2−2)=3(0)=0
So, x=2 is the zero of the polynomial p(x).
(v) p(x)=x
2
Put x=0, we get
p(x)=(0)
2
=0
So, x=0 is the zero of the polynomial p(x).
(vi) p(x)=lx+m
Put x=−
l
m
, we get
p(x)=l(−
l
m
)+m=−m+m=0
So, x=−
l
m
is the zero of the polynomial p(x).
(vii) p(x)=3x
2
−1
Put x=−
3
1
, we get
p(x)=3(−
3
1
)
2
−1=(3×
3
1
)−1=0
So, x=−
3
1
is the zero of the polynomial p(x).
Put x=
3
2
, we get
p(x)=3(
3
2
)
2
−1=(3×
3
4
)−1=3
=0
So, x=
3
2
is not the zero of the polynomial p(x).
(viii) p(x)=2x+1
Put x=
2
1
, we get
p(x)=2(
2
1
)+1=1+1=2
=0
So, x=
2
1
is not the zero of the polynomial p(x).