# What is the length and width of a rectangle with an area of 2x^2 + x - 3?

Apr 16, 2016

The length and width can be:

$\left\{\begin{matrix}k \left(2 x + 3\right) \\ \frac{1}{k} \left(x - 1\right)\end{matrix}\right.$ for any $k > 0$

#### Explanation:

I think this is a really bad question, since there are normally infinitely many solutions for a given value of $x$.

$2 {x}^{2} + x - 3 = \left(x - 1\right) \left(2 x + 3\right)$

So the length could be $k \left(2 x + 3\right)$ and the width $\frac{1}{k} \left(x - 1\right)$ for any $k > 0$

What we can say is that this will only be a (non-degenerate) rectangle if $x > 1$.