Verify whether the following are zeroes of the polynomial, indicated against them.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii)
(viii)
(i) If x = 
is a zero of polynomial p(x) = 3x + 1 then p (
) should be 0
At, 
= -1 + 1 = 0
Therefore, x = –1/3 is a zero of polynomial p(x) = 3x + 1
(ii) If x = 
is a zero of polynomial p(x) = 5x - π then p (
) should be 0
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) = x2 - 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) = x2 - 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) = x2
Then, p (0) should be zero
Here, p (0) = (0)2 = 0
Hence, x = 0 is the zero of the polynomial p (x) = x2
(vi) If x = 
is a zero of the polynomial (x) = lx + m then p (
) should be 0
At, p (
) = l (
) + m = - m + m = 0
Therefore, x = 
is the zero of the polynomial p(x) = lx + m
(vii) If x = 
and x = 
are zeros of the polynomial p (x) = 3x2 – 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) = 3x2 + 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