Answer :

After substituting the value for variable in the polynomial if we get 0 then that value is called zero of the polynomial

Here we have to equate the polynomial to 0 to get the zeroes of that polynomial

i. p(x) = x – 4

⇒ x – 4 = 0

⇒ x = 4

Hence x = 4 is zero of polynomial p(x) = x – 4

ii. p(x) = 4x

⇒ 4x = 0

⇒ x = 0

Hence x = 0 is zero of polynomial p(x) = 4x

iii. p(x) = bx, b ≠ 0

⇒ bx = 0

⇒ b = 0 or x = 0 or both

But given that b ≠ 0 hence x has to be 0

⇒ x = 0

Hence x = 0 is zero of polynomial p(x) = bx

iv. p(x) = x + 3

⇒ x + 3 = 0

⇒ x = -3

Hence x = -3 is zero of polynomial p(x) = x + 3

v. p(x) = 2x – 1

⇒ 2x – 1 = 0

⇒ 2x = 1

Hence is zero of polynomial p(x) = 2x – 1

vi. p(x) = 3x + 7

⇒ 3x + 7 = 0

⇒ 3x = -7

Hence is zero of polynomial p(x) = 3x + 7

vii. p(x) = cx + d, c ≠ 0, c, d are real numbers.

⇒ cx + d = 0

⇒ cx = -d

Hence is zero of polynomial p(x) = cx + d

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