Option 3 : 1 : 3

__Concept:__

Conversely, if (x - a) is a factor of p(x), then p(a) = 0.

**Calculation:**

Let f(x) = sx2 - 3x - t be the given polynomial. Since (x - 1) and (x + 3) are factors of f(x).

∴ f(1) = 0 and f(-3) = 0

Now, we have f(1) = 0

⇒ s(1)2 - 3(1) - t = 0

⇒ s - 3 - t = 0

⇒ s - t = 3 ----(1)

Also, f(-3) = 0

⇒ s(-3)2 - 3(-3) - t = 0

⇒ 9s + 9 - t = 0

⇒ 9s - t = -9 ----(2)

On multiplying equation (1) by -3, we get

-3s + 3t = -9 ----(3)

Now, the RHS of equations (2) & (3) are same,

⇒ 9s - t = -3s + 3t

⇒ 12s = 4t

⇒ 3s = t

⇒ s/t = 1/3

**⇒ s : t = 1 : 3**