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Assoli18 [71]
3 years ago
13

Create a 3rd degree polynomial function with one zero at three. Sketch a graph

Mathematics
1 answer:
DedPeter [7]3 years ago
4 0

Answer:

f(x) =  {x}^{3}  - 9 {x}^{2}  + 27x - 27

Step-by-step explanation:

We want to create a third degree polynomial function with one zero at three.

In other words, we want to find a polynomial function with roots x=3 , multiplicity, 3.

Since x=3 is a solution, x-3 is the only factor that repeats thrice.

f(x) =  {(x - 3)}^{3}

We expand to get:

f(x) =  x( {x}^{2}  - 6x  + 9) - 3( {x}^{2}  - 6x + 9)

f(x) =  {x}^{3}  - 6 {x}^{2}  + 9x- 3 {x}^{2}   + 18x  - 27

This simplifies to:

f(x) =  {x}^{3}  - 9 {x}^{2}  + 27x - 27

See attachment for graph.

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Step-by-step explanation:

Given:

A box has a volume of 308 cm cubed.

Its height is 4 cm greater than its length.

Its length is 3 cm greater than its width.

Question asked:

What is the width of the box?

<u>Solution</u>:

Let width  = x\ cm

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<u>As we know:</u>

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By substituting the value:-

Width  = x\ cm = 4 cm

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