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# 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.