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.

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.