If α ≠ β but α^{2} = 5α - 3 and β^{2} = 5β - 3, then the equation having α/β and β/α as its roots is

- 3x
^{2}- 19x - 3 = 0 - 3x
^{2}- 19x + 3 = 0 - x
^{2}- 5x + 3 = 0 - 3x
^{2}+ 19x - 3 = 0

**Solution**

The equation having α and β as its root will be:

x^{2} - (α+β)x + αβ = 0 and since α^{2} = 5α-3 and β^{2} = 5β-3 shows that α and β are roots of equation

x^{2} - 5x + 3 = 0 this implies α+β = 5 and αβ = 3

You can use these relations to calculate the equation having α/β and β/α as its root.

(α/β)*(β/α) = 1 and β/α + α/β = 19/3

Therefore, the equation is 3x^{2} - 19x + 3 = 0

**The correct option is B.**