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The area of a rectangular rug is given by the trinomial r^2-4r-21. What are the possible dimensions of the rug?

User Arkentos
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1 Answer

4 votes

Answer:

There are two possible values for r (area): r =-7 or r=3

Explanation:

Given the rectangular rug area is:


r^(2) -4r -21

We have to convert the above equation into factored form.

So two numbers whose product is -21r² and sum is -4r

<=>
r^(2) -4r -21

=
r^(2) -7r + 3r -21

= r (r -7) + 3(r -7)

= (r-7)(r+3)

We set
r^(2) -4r -21 = 0

<=> (r-7)(r+3) = 0

<=> (r-7) = 0 or (r+3) = 0

<=> r =-7 or r=3

So, there are two possible values for r (area): r =-7 or r=3

User Harout
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