Given $$2x^2 + 19x + 45 = 0$$​ and $$2y^2 + 11y + 12 = 0$$​, then which of the following regarding the roots x, y is TRUE?

Two quadratic equations:

​$$2x^2 + 19x + 45 = 0 …………. (i)$$​​

​$$2y^2 + 11y + 12 = 0 ………….(ii)$$​​

For equation (1).

​$$2x^2 + 19x + 45 = 0$$​​

​$$2x^2 + 10x + 9x + 45 = 0$$​​

2x(x + 5) + 9(x + 5) = 0

(2x + 9)(x + 5) = 0

2x + 9 = 0 or x + 5 = 0

x = $$\frac{-9}{2}$$​ = -4.5 or x = -5

x = -4.5, -5

For equation (2)

​$$2y^2 + 11y + 12 = 0$$​​

​$$2y^2 + 8y + 3y + 12 = 0$$​​

2y( y + 4) + 3(y + 4) = 0

(2y + 3)(y + 4) = 0

2y + 3 = 0 or y + 4 = 0

y = $$\frac{-3}{2}$$​= - 1.5 or y = - 4

y = -1.5, -4

Now, comparing values of x and y

x = -4.5, -5

y = -1.5, -4

Thus, we can see x < y.