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nydimaria [60]
3 years ago
12

Which of the following is a polynomial with roots 5,7 and -8

Mathematics
2 answers:
Aloiza [94]3 years ago
3 0

The idea is to use the zero product property in reverse to go from the roots to the factorization. Then you expand out the polynomial using the distributive property.

x = 5 or x = 7 or x = -8

x-5 = 0 or x-7 = 0 or x+8 = 0

(x-5)(x-7)(x+8) = 0

(x-5)(x^2+x-56) = 0

x(x^2+x-56) - 5(x^2+x-56) = 0

x^3+x^2-56x  -5x^2-5x+280 = 0

x^3-4x^2-61x+280 = 0

f(x) = x^3 - 4x^2 - 61x + 280

<h3>Answer: Choice D</h3>
zloy xaker [14]3 years ago
3 0

Answer:

The correct answer is option 4). x³- 4x² -61x + 280

Step-by-step explanation:

It is given that, a polynomial with roots 5,7 and -8

<u>To find the polynomial</u>

The roots are 5,7 and -8

Then the factors are, (x-5), (x-7) and (x+8)

p(x) = (x-5)(x-7)(x+8) = (x-5)(x² + 8x -7x + 56)

= (x-5)(x² + x - 56)

= x³ + x² - 56x -5x² - 5x + 280

= x³- 4x² -61x + 280

Therefore the polynomial is p(x) = x³- 4x² -61x + 280

The correct answer is option 4). x³- 4x² -61x + 280

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The total length of a line segment is the sum of the lengths of its parts.

MQ = MK + KQ . . . . . . express the relationship between the segments

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Determine the most precise name for the quadrilateral,
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Answer: Choice C

\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}0 & 1\\\cline{1-2}2 & 2\\\cline{1-2}4 & 3\\\cline{1-2}6 & 4\\\cline{1-2}\end{array}

=========================================================

Explanation:

There are four marked points on the line.

Each point is of the form (x,y)

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Each of these points is then listed in the table format as shown above.

There are infinitely many other points on the line; however, we only select a few of them to make the table (or else we'd be here all day).

Extra side notes:

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  • The equation of this line is y = 0.5x+1
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