Find the zero of the polynomial in each of the following cases: \( \begin{array}{lll}\text { (i) } p(x)=x-5 & \text { (ii) } p(x)=x-5 & \text { (iii) } p(x)=2 x+5 \\ \text { (iv) } p(x)=3 x-2 & \text { (v) } p(x)=3 x & \text { (vi) } p(x)=a x, a \neq 0 \\ \text { (vii) } p(x)=c x+d, c \neq 0, c, d \text { are real numbers. } & \end{array} \)

To find the zeros of the given polynomials, we set each polynomial \( p(x) \) equal to zero and solve for \( x \). ### (i) \( p(x) = x - 5 \) Set \( p(x) = 0 \): \[ x - 5 = 0 \implies x = 5 \] **Zero:** \( x = 5 \) ### (ii) \( p(x) = x - 5 \) This is identical to part (i). **Zero:** \( x = 5 \) ### (iii) \( p(x) = 2x + 5 \) Set \( p(x) = 0 \): \[ 2x + 5 = 0 \implies 2x = -5 \implies x = -\frac{5}{2} \] **Zero:** \( x = -\frac{5}{2} \) ### (iv) \( p(x) = 3x - 2 \) Set \( p(x) = 0 \): \[ 3x - 2 = 0 \implies 3x = 2 \implies x = \frac{2}{3} \] **Zero:** \( x = \frac{2}{3} \) ### (v) \( p(x) = 3x \) Set \( p(x) = 0 \): \[ 3x = 0 \implies x = 0 \] **Zero:** \( x = 0 \) ### (vi) \( p(x) = ax \), where \( a \neq 0 \) Set \( p(x) = 0 \): \[ ax = 0 \implies x = 0 \] **Zero:** \( x = 0 \) ### (vii) \( p(x) = cx + d \), where \( c \neq 0 \) and \( c, d \) are real numbers Set \( p(x) = 0 \): \[ cx + d = 0 \implies cx = -d \implies x = -\frac{d}{c} \] **Zero:** \( x = -\frac{d}{c} \) --- **Summary of Zeros:** 1. **(i) and (ii):** \( x = 5 \) 2. **(iii):** \( x = -\frac{5}{2} \) 3. **(iv):** \( x = \frac{2}{3} \) 4. **(v) and (vi):** \( x = 0 \) 5. **(vii):** \( x = -\frac{d}{c} \)