Answer :

For any value of x, say a, to be a zero of polynomial p(a) = 0

Keeping that in mind,**(i)** Here p(x)= 3x + 1 , for x = -1/3

Therefore, x = –1/3 is a zero of polynomial p(x) = 3x + 1

**(ii)** here p(x) = 5x - π, for x = 4/5,

Since,

Therefore, x = 4/5 is not a zero of polynomial p(x) = 5x - π

**(iii)** If x = 1 and x = -1 are zeros of polynomial p(x) = x^{2} - 1 then p (1) and p (-1) should be 0

At, p (1) = (1)^{2} – 1 = 0 and,

At, p (-1) = (-1)^{2} – 1 = 0

Hence, x = 1 and -1 are zeros of polynomial p (x) = x^{2} - 1

**(iv)** If x = -1 and x = 2 are zeros of polynomial p(x) = (x + 1) (x – 2) then p (-1) and p (2) should be 0

At, p (-1) = (-1 + 1) (- 1 – 2) = 0 (-3) = 0 and,

At, p (2) = (2 + 1) (2 – 2) = 3 (0) = 0

Hence, x = -1 and x = 2 are zeros of polynomial p (x) = (x + 1) (x – 2)

**(v)** If x = 0 is a zero of polynomial p (x) = x^{2}

Then, p (0) should be zero

Here, p (0) = (0)^{2} = 0

Hence, x = 0 is the zero of the polynomial p (x) = x^{2}

**(vi)** If x = is a zero of the polynomial p(x) = lx + m then p () should be 0

Therefore, x = is the zero of the polynomial p(x) = l x + m

**(vii)** If x = and x = are zeros of the polynomial p(x) = 3 x^{2} – 1, then

p() and p() should be 0

At, p () = 3 ()^{2} – 1

= 3 () – 1

= 1 – 1 = 0 and,

At, p () = 3 ()^{2} – 1

= 3 () – 1

= 4 – 1 = 3

Therefore, x = is a zero of the polynomial p(x) = 3x^{2} + 1

But, x = is not a zero of the polynomial

**(viii)** If x = is a zero of polynomial p (x) = 2x + 1 then p(1/2) should be zero

At, p () = 2 () + 1

= 1 + 1 = 2

Therefore, x = is not a zero of given polynomial p(x) = 2x + 1

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