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maxonik [38]
3 years ago
5

The rectangular floor of a closet is divided into two right triangles by drawing a diagonal. One leg of the right triangle is 11

foot less than twicethan twice the other leg. The hypotenuse is 17 feet. Determine the​ closet's length and width. Let the width be the shorter side.
Mathematics
1 answer:
AysviL [449]3 years ago
5 0
W = width 
<span>2w + 2 = length </span>
<span>w^2 + (2w + 2)^2 = 13^2 </span>
<span>w^2 + 4w^2 + 8w + 4 - 169 = 0 </span>
<span>5w^2 + 8w - 165 = 0 </span>
<span>(5w + 33)(w - 5) = 0 </span>
<span>w = 5 ft width </span>
<span>2(5) + 2 = 12 ft length</span>
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Simplest polynomial function is x^4-x^3-11x^2+9x+18.

Solution:

Given data:

Zeroes are 3i, –1, 2.

3i is a complex root of the function.

If 3i is a zero of the polynomial then –3i is also a zero of the polynomial.

Therefore zeroes are 3i, –3i –1, 2.

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            =(x^2+3ix-3ix+(3i)^2)(x^2-2x+x-2)

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Since the value of i^2=-1

            =x^2(x^2-x-2)-9(x^2-x-2)

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