Verify that:
(i) 4 is a zero of the polynomial p(x)=x-4.
(ii) -3 is a zero of the polynomial p(x) = x + 3.
(iii) -1/2 is a zero of the polynomial p(y)=2y+1.
(iv) 2/5 is a zero of the polynomial p(x) =2-5x.
(v) 1 and 3 are the zeros of the polynomial p(x)=(x-1)(x-2)
(vi) 0 and 3 are the zeros of the polynomial p(x) =x2 - 3x
(vii) 2 and-3 are the zeros of the polynomial p(x) =x2 + x - 6
(i) We have, p(x) = x – 4
In order to verify the zero of the polynomial,
Put p(x) = 4
put x = 4 in the expression , we get,
p(4) = 4 – 4
p(4) = 0
Since p(4) = 0
Hence, 4 is a zero of the polynomial p(x).
(ii) We have, p(x) = x + 3
In order to verify the zero of the polynomial,
Put p(x) = -3
p(-3) = - 3 + 3
p(-3) = 0
Since p(-3) = 0
Hence, -3 is a zero of the polynomial p(x).
(iii) We have, p(y) = 2y + 1
In order to verify the zero of the polynomial,
Put p(y) = 1/2
p(1/2) = 2(1/2) + 1
p(1/2) = 1 + 1
p(1/2) = 2
Since p(1/2) ≠ 0
Hence, 1/2 is not a zero of the polynomial p(y)
(iv) We have, p(x) = 2 - 5x
In order to verify the zero of the polynomial,
Put p(x) = 2/5
p(2/5) = 2 - 5 (2/5)
p(2/5)= 2 - 2
p(2/5)= 0
Since p(2/5) = 0
Hence, 2/5 is a zero of the polynomial p(x)
(v) We have, p(x) = (x-1)(x-2)
In order to verify the zero of the polynomial,
Case 1: Put x = 1, we get,
p(1) = (1-1)(1-2)
p(1) = 0(-1)
p(1) = 0
Hence, 1 is a zero of the polynomial p(x)
Case 2: Put x = 3, we get,
p(3) = (3-1)(3-2)
p(3) = 2(1)
p(3) = 2
since p(3) ≠ 3
Hence, 3 is not a zero of the polynomial p(x)
(vi) We have, p(x) = x2 -3x
In order to verify the zero of the polynomial,
Case 1: Put x = 0
p(0) = (0)2 – 3(0)
p(0) = 0 - 0
p(0) = 0
Since p(0) = 0
Hence, 0 is a zero of the polynomial p(x)
Case 2: Put x = 3
p(3) = (3)2 – 3(3)
p(3) = 9 - 9
p(3) = 0
Since p(3) = 0
Hence, 3 is a zero of the polynomial p(x)
(vii) We have, p(x) =x2 + x - 6
In order to verify the zero of the polynomial,
Case 1: Put x = 2
p(2) = (2)2 + 2 - 6
p(2) = 4 + 2 - 6
p(2) = 0
Since p(2) = 0
Hence, 2 is a zero of the polynomial p(x)
Case 2: Put x = -3
p(3) = (-3)2 + (–3) – 6
p(3) = 9 - 3 - 6
p(3) = 0
Since p(-3) = 0
Hence, -3 is a zero of the polynomial p(x)