Find the zero of the polynomial :
`p(x)=x-5`
(ii) `q(x)=x+4`
(iii) `r(x)=2x+5`
(iv) `f(x)=3x+1`
(v) `g(x)=5-4x`
(vi) `h(x)=6x-2`
(vii) `p(x)=ax,ane0`
(viii) `q(x)=4x`

Answer

To find the zero of the given polynomials, we need to set each polynomial equal to zero and solve for \( x \). Let's go through each polynomial step by step.

### Step-by-Step Solutions:

1. **Polynomial:** \( p(x) = x - 5 \)
**Set it to zero:**
\[ x - 5 = 0 \]
**Solve for \( x \):**
\[ x = 5 \]
**Zero of \( p(x) \):** \( 5 \)

2. **Polynomial:** \( q(x) = x + 4 \)
**Set it to zero:**
\[ x + 4 = 0 \]
**Solve for \( x \):**
\[ x = -4 \]
**Zero of \( q(x) \):** \( -4 \)

3. **Polynomial:** \( r(x) = 2x + 5 \)
**Set it to zero:**
\[ 2x + 5 = 0 \]
**Solve for \( x \):**
\[ 2x = -5 \quad \Rightarrow \quad x = -\frac{5}{2} \]
**Zero of \( r(x) \):** \( -\frac{5}{2} \)

4. **Polynomial:** \( f(x) = 3x + 1 \)
**Set it to zero:**
\[ 3x + 1 = 0 \]
**Solve for \( x \):**
\[ 3x = -1 \quad \Rightarrow \quad x = -\frac{1}{3} \]
**Zero of \( f(x) \):** \( -\frac{1}{3} \)

5. **Polynomial:** \( g(x) = 5 - 4x \)
**Set it to zero:**
\[ 5 - 4x = 0 \]
**Solve for \( x \):**
\[ 4x = 5 \quad \Rightarrow \quad x = \frac{5}{4} \]
**Zero of \( g(x) \):** \( \frac{5}{4} \)

6. **Polynomial:** \( h(x) = 6x - 2 \)
**Set it to zero:**
\[ 6x - 2 = 0 \]
**Solve for \( x \):**
\[ 6x = 2 \quad \Rightarrow \quad x = \frac{2}{6} = \frac{1}{3} \]
**Zero of \( h(x) \):** \( \frac{1}{3} \)

7. **Polynomial:** \( p(x) = ax \) (where \( a \neq 0 \))
**Set it to zero:**
\[ ax = 0 \]
**Solve for \( x \):**
\[ x = 0 \]
**Zero of \( p(x) \):** \( 0 \)

8. **Polynomial:** \( q(x) = 4x \)
**Set it to zero:**
\[ 4x = 0 \]
**Solve for \( x \):**
\[ x = 0 \]
**Zero of \( q(x) \):** \( 0 \)

### Summary of Zeros:
1. \( p(x) = x - 5 \) → Zero is \( 5 \)
2. \( q(x) = x + 4 \) → Zero is \( -4 \)
3. \( r(x) = 2x + 5 \) → Zero is \( -\frac{5}{2} \)
4. \( f(x) = 3x + 1 \) → Zero is \( -\frac{1}{3} \)
5. \( g(x) = 5 - 4x \) → Zero is \( \frac{5}{4} \)
6. \( h(x) = 6x - 2 \) → Zero is \( \frac{1}{3} \)
7. \( p(x) = ax \) → Zero is \( 0 \)
8. \( q(x) = 4x \) → Zero is \( 0 \)