Write a polynomial that has the lowest degree, a leading coefficient of 2, and 1/2 and 3 + √5 as roots?

1 answer:

3 0

$2\left(x-\dfrac{1}{2}\right)(x-(3+\sqrt5))=\\
(2x-1)(x-3-\sqrt5)=\\
2x^2-6x-2\sqrt5x -x+3+\sqrt5=\\
2x^2-(7+2\sqrt5)x+3+\sqrt5$

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Mario is setting up a new tent during a camping trip. The tent came with 7 feet of rope. The instructions are to use 34.5 inches

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An equation is formed of two equal expressions. The number of sections that Mario can cut from the rope is 6.

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An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of 8 1/4 - inch sections of rope Mario can cut from the rope be x.

Since the total length of the rope is 7 feet, which is equal to 84 inches(1 foot=12 inches), the instructions are to use 34.5 inches of the rope to tie a tarp on top of the tent. Therefore, the rope for the 8 1/4 inches section is,

Rope left = 84 inches - 34.5 inches

Since the length of a single section is 8 1/4 inches(8.25 inches), therefore the number of sections that can be made from the remaining section is,

The number of sections, n = Rope left/8.25 inches

= (84 -34.5)inches /8.25 inches

= 6

Hence, the number of sections that Mario can cut from the rope is 6.

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