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

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Answer 1 · 2016-04-16T22:53:33

The length and width can be:

#{ (k(2x+3)), (1/k(x-1)) :}# for any #k > 0#

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

#2x^2+x-3 = (x-1)(2x+3)#

So the length could be #k(2x+3)# and the width #1/k(x-1)# for any #k > 0#

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