Answer: [tex]\forall \alpha \in \mathbb{R}_+^* : (\frac{x+5}{\alpha},\alpha(x-0.5))[/tex]

Step-by-step explanation:

We first calculate the zeros of this expression :

Δ = 9² - 4(2*(-5)) = 81 + 40 = 121 and √Δ = 11

so the zeros are -5 and 0.5.

Hence, 2x²+9x-5​ = (x+5)(x-0.5)

We can write the possible values for (lenght,breadth) as follows :

[tex]\forall \alpha \in \mathbb{R}_+^* : (\frac{x+5}{\alpha},\alpha(x-0.5))[/tex]