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Answer :
i) We have, \(p(x) = x + 5\)
We also know that, if p(x) = 0 then x is the Zero of the polynomial.
\(\therefore p(x) = 0 \)
\(\Rightarrow x + 5 = 0 \)
\(\Rightarrow x = -5 \)
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.
\(\therefore p(x) = 0 \)
\(\Rightarrow x - 5 = 0\)
\(\Rightarrow x = 5 \)
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.
\(\therefore, p(x) = 0 \)
\(\Rightarrow 2x + 5 = 0\)
\(\Rightarrow x = \frac{-5}{2} \)
Hence,\(\frac{-5}{2} \) 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.
\(\therefore p(x) = 0 \)
\(\Rightarrow 3x - 2 = 0\)
\(\Rightarrow x = \frac{2}{3} \)
Hence, \(\frac{2}{3} \) 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.
\(\therefore p(x) = 0 \)
\(\Rightarrow 3x = 0\)
\(\Rightarrow x = 0 \)
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.
\(\therefore p(x) = 0 \)
\(\Rightarrow ax = 0\)
\(\Rightarrow x = 0, a \ne 0\)
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.
\(\therefore p(x) = 0 \)
\(\Rightarrow cx + d = 0\)
\(\Rightarrow x = \frac{-d}{c} , c \ne 0\)
Hence, \(\frac{-d}{c} \) is the zero of given ploynomial.