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

Answer 1

Genesis Allen

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#.

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Answer 2

Jace Anderson

To find the length and width of the rectangle with an area of (2x^2 + x - 3), we need to factor the quadratic expression into two binomials. Once factored, we can interpret the factors as the length and width of the rectangle. Factoring the quadratic expression (2x^2 + x - 3), we get ((2x - 3)(x + 1)). Therefore, the length of the rectangle is (2x - 3) and the width is (x + 1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.