Math, asked by umapainkra5, 6 months ago

verify whether x=-1/√3, 2/√3 are zeroes of polynomial p(x)=3x²-1​

Answers

Answered by nikhilngare350
4

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).

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