Verify that
(i) 3 is a zero of the polynomial x-5.
(ii) -2 is a zero of the polynomial x+2.
`(iii) (7)/(3)` is a zero of the polynomial 3x-7.
(iv) 2 and 3 are zeros of the polynomial (x-2)(x-3).
`(v) (13)/(2)` and -3 are zeros of the polynomial `2x^(2)-7x-39`.

Answer

To verify whether the given numbers are zeros of the respective polynomials, we will substitute each number into the polynomial and check if the result is zero.

### Solution:

**(i)** Verify if 3 is a zero of the polynomial \( x - 5 \).

1. Substitute \( x = 3 \) into the polynomial:
\[ 3 - 5 = -2 \]
2. Since \(-2 \neq 0\), 3 is **not** a zero of the polynomial \( x - 5 \).

**(ii)** Verify if -2 is a zero of the polynomial \( x + 2 \).

1. Substitute \( x = -2 \) into the polynomial:
\[ -2 + 2 = 0 \]
2. Since \(0 = 0\), -2 **is** a zero of the polynomial \( x + 2 \).

**(iii)** Verify if \( \frac{7}{3} \) is a zero of the polynomial \( 3x - 7 \).

1. Substitute \( x = \frac{7}{3} \) into the polynomial:
\[ 3 \left(\frac{7}{3}\right) - 7 = 7 - 7 = 0 \]
2. Since \(0 = 0\), \( \frac{7}{3} \) **is** a zero of the polynomial \( 3x - 7 \).

**(iv)** Verify if 2 and 3 are zeros of the polynomial \( (x - 2)(x - 3) \).

1. Substitute \( x = 2 \):
\[ (2 - 2)(2 - 3) = 0 \cdot (-1) = 0 \]
2. Since \(0 = 0\), 2 **is** a zero of the polynomial.

3. Substitute \( x = 3 \):
\[ (3 - 2)(3 - 3) = 1 \cdot 0 = 0 \]
4. Since \(0 = 0\), 3 **is** a zero of the polynomial.

**(v)** Verify if \( \frac{13}{2} \) and -3 are zeros of the polynomial \( 2x^2 - 7x - 39 \).

1. Substitute \( x = -3 \):
\[ 2(-3)^2 - 7(-3) - 39 = 2(9) + 21 - 39 = 18 + 21 - 39 = 0 \]
2. Since \(0 = 0\), -3 **is** a zero of the polynomial.

3. Substitute \( x = \frac{13}{2} \):
\[ 2\left(\frac{13}{2}\right)^2 - 7\left(\frac{13}{2}\right) - 39 \]
\[ = 2 \cdot \frac{169}{4} - \frac{91}{2} - 39 \]
\[ = \frac{338}{4} - \frac{182}{4} - \frac{156}{4} \]
\[ = \frac{338 - 182 - 156}{4} = \frac{0}{4} = 0 \]
4. Since \(0 = 0\), \( \frac{13}{2} \) **is** a zero of the polynomial.

### Summary:
- (i) 3 is **not** a zero of \( x - 5 \).
- (ii) -2 **is** a zero of \( x + 2 \).
- (iii) \( \frac{7}{3} \) **is** a zero of \( 3x - 7 \).
- (iv) 2 and 3 **are** zeros of \( (x - 2)(x - 3) \).
- (v) \( \frac{13}{2} \) and -3 **are** zeros of \( 2x^2 - 7x - 39 \).