Question

Verify whether the following are zeroes of the polynomial, indicated against them.

(i) p(x) = 3x + 1, x = -1/3

(ii)  p(x) = 5x - π, x = 4/5

(iii) p(x) = x2 - 1, x = 1, -1

(iv) p(x) = (x + 1) (x - 2), x = -1, 2

(v) p(x) = x2 , x = 0

(vi) p(x) = 2x + 1, x = 1/2

Answer 1

Hii..

We know that a real number k is said to be a zero of a polynomial p(x), if p(k)=0.

So, here is your answer......

(i) p(x)= 3x+1
p(-1/3)= 3* -1/3 + 1
= -1+1
= 0
Since p(-1/3)=0
Therefore, x= -1/3 is a zero of the polynomial
p(x).

ii) p(x)= 5x - pi
x=4/5
p(4/5)= 5*4/5 - 22/7
= 4 - 22/7
= 6/7
Since p(4/5) is not equal to 0,
therefore x= 4/5 is not a zero of the polynomial p(x).

iii) p(x) = x2 - 1
x = 1, -1
p(1)= 1-1
= 0
Since p(1)= 0
Therefore x=1 is a zero the polynomial p(x).
p(-1) = (-1)^2 - 1
= 1 - 1
= 0
Since p(-1)= 0,
Therefore x=-1 is a zero of the polynomial p(x).

iv) p(x)= (x+1) (x-2)
= x^2 -2x + x -2
p(x) =x^2 -x -2
p(-1) = (-1)^2 -1 -2
= 1 - 1 -2
= -2
Since p(-1) is not equal to zero,
Therefore x= -1 is not a zero of p(x).
p(2)= (2)^2 - 2 -2
= 4-4
=0
Since p(2)= 0,
Therefore x=2 is a zero of the polynomial p(x).

v) p(x) = x^2
p(0)= (0)^2
p(0)= 0
Since p(0)= 0,
Therefore x=0 is a zero of the polynomial p(x)

vi) p(x)= 2x +1
x= 1/2
p(1/2)= 2* 1/2 +1
= 1 + 1
= 2
Since p(1/2) is not equal to zero,
Therefore x=1/2 is not a zero of 2x+1

Hope it helps you......

Thanks..... :)

Answer 2

Hey there !!!!!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Zero of the polynomial of P(x)  is value of variable "x" at which P(x) = 0

~~~~~~~~~~~~~~~~~~~

1) p(x) = 3x + 1, x = -1/3

    p(-1/3) = -3/3 + 1 = -1+1 = 0

So x=-1/3 is a zero of polynomial of p(x) 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2) p(x) = 5x-π at x= 4/5

    p(4/5) = 4-π≠0

So 4/5 is not a zero of polynomial of p(x) 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3) p(x) = x² - 1, x = 1, -1 

    p(1) = 1-1 = p(-1) =1-1 =0

So 1,-1 are zeroes fo polynomial for p(x)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

4) p(x) = (x + 1) (x - 2), x = -1, 2

    p(-1) = (-1+1)(-3) = 0 = p(2) = (3)(2-2) =0

So, 2,-1 are zeroes fo polynomial for p(x)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

5) p(x) = x²

    p(0) = 0 So "0" is a zero of polynomial of p(x)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

6) p(x) = 2x+1

    p(1/2) = 2/2 + 1 = 2 ≠ 0

So, 1/2 is not a zero pf polynomial of p(x)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helped you......................