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Explanation:

We know that the sum of the roots = $-\frac{b}{a}$.

Hence, x₁ + x₂ = 2. Now we have two equations, viz. x₁ + x₂ = 2 ...(i)
and 7x₂ – 4x₁ = 47 ...(ii)

Solving these two equations, we get x₁ = –3 and x₂ = 5. Since it does not satisfy options (b) and (c), we will verify it for option (a). 

The product of the roots = (–3) × 5 = –15, $\frac{c}{a}$ in our case is c. Hence, c = –15.

Alternately,
Put values of x₁, x₂ in equation (ii). Do not match. So put c = –15 in equation (i) to get the roots of equation. After finding the roots of equation (i), check whether they satisfy equation (ii) or not. 

The roots (5, –3) satisfy the equation (ii) so answer is (a).

Hence, option (a).