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4. Find the Zero of the polynomial in each of the following cases.
i)\(p(x) = x + 5\)
ii)\(p(x) = x - 5\)
iii)\(p(x) = 2x + 5\)
iv)\(p(x) = 3x - 2\)
v)\(p(x) = 3x\)
vi)\(p(x) = ax, a \ne 0\)
vii)\(p(x) = cx + d ,c \ne 0\), c,d, are real numbers.
Answer :

i)We have, \(p(x) = x + 5\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
Therefore, p(x) = 0
i.e. \(x + 5 = 0\)
i.e. x = -5
Hence, -5 is the zero of given ploynomial.

ii)We have, \(p(x) = x - 5\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
Therefore, p(x) = 0
i.e. \(x - 5 = 0\)
i.e. x = 5
Hence, 5 is the zero of given ploynomial.

iii)We have, \(p(x) = 2x + 5\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
Therefore, p(x) = 0
i.e. \(2x + 5 = 0\)
i.e. x = -5/2
Hence, -5/2 is the zero of given ploynomial.

iv)We have, \(p(x) = 3x - 2\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
Therefore, p(x) = 0
i.e. \(3x - 2 = 0\)
i.e. x = 2/3
Hence, 2/3 is the zero of given ploynomial.

v)We have, \(p(x) = 3x\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
Therefore, p(x) = 0
i.e. \(3x = 0\)
i.e. x = 0
Hence, 0 is the zero of given ploynomial.

vi)We have, \(p(x) = ax\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
Therefore, p(x) = 0
i.e. \(ax = 0\)
i.e.\( x = 0, a \ne 0\)
Hence, 0 is the zero of given ploynomial.

vii)We have, \(p(x) = cx + d\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
Therefore, p(x) = 0
i.e. \(cx + d = 0\)
i.e.\( x = -d/c, c \ne 0\)
Hence, -d/c is the zero of given ploynomial.