Given information:
- The polynomial is 5x^2 + 7x + 2.
- The zeroes of the polynomial are α and β.

To find the sum of their reciprocals, we need to find the values of 1/α and 1/β.

Using the zero product property, we know that if α and β are zeroes of the polynomial, then (x - α) and (x - β) are factors of the polynomial.

So, we can write the polynomial as:

5x^2 + 7x + 2 = 0

(x - α)(x - β) = 0

Expanding the above expression, we get:

x^2 - (α + β)x + αβ = 0

Comparing the coefficients of the terms on both sides, we can equate them.

Coefficient of x^2: 1 = 5
Coefficient of x: -(α + β) = 7
Constant term: αβ = 2

We are given that the zeroes are α and β, so we can write:

α + β = -7 (Equation 1)
αβ = 2 (Equation 2)

To find 1/α and 1/β, we can take the reciprocal of both sides of Equation 1 and Equation 2.

Reciprocating Equation 1, we get:

1/(α + β) = -1/7

Reciprocating Equation 2, we get:

1/(αβ) = 1/2

So, 1/α + 1/β = -1/7 + 1/2

To add these fractions, we need to find their least common denominator (LCD), which is 14.

Multiplying the numerator and denominator of -1/7 by 2, we get -2/14.

So, -1/7 + 1/2 = -2/14 + 7/14 = (7 - 2)/14 = 5/14

Therefore, 1/α + 1/β = 5/14.

But we need to find the sum of α and β, not their reciprocals.

Recall Equation 1: α + β = -7

So, we need to find 1/(-7).

Taking the reciprocal, we get -1/7.

Therefore, 1/α + 1/β = 5/14 and α + β = -7.

So, the correct answer is option D) 7/2.