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Alborosie
3 years ago
5

Write a third degree polynomial function that has real zeros -1, -2 and 4

Mathematics
1 answer:
ra1l [238]3 years ago
8 0

Answer:

f(x) = x^{3}  - x^{2}  -  10x  -8

Step-by-step explanation:

All you have to do is multiply (x + 1)(x + 2)(x - 4)

You should get x^{3}  - x^{2}  -  10x  -8

So,  f(x) = x^{3}  - x^{2}  -  10x  -8

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PLEASE HELP 100 POINTS!!!!!!
horrorfan [7]

Answer:

A)  See attached for graph.

B)  (-3, 0)  (0, 0)  (18, 0)

C)   (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.

Given piecewise function:

g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad  \textsf{if }x\geq 3\end{cases}

Therefore, the function has two definitions:

  • g(x)=x^3-9x \quad \textsf{when x is less than 3}
  • g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}

<h3><u>Part A</u></h3>

When <u>graphing</u> piecewise functions:

  • Use an open circle where the value of x is <u>not included</u> in the interval.
  • Use a closed circle where the value of x is <u>included</u> in the interval.
  • Use an arrow to show that the function <u>continues indefinitely</u>.

<u>First piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

\implies g(3)=(3)^3-9(3)=0 \implies (3,0)

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

<u>Second piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

<h3><u>Part B</u></h3>

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the <u>first piece</u> of the function to zero and solve for x:

\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the <u>second piece</u> to zero and solve for x:

\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}

\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b

\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

<h3><u>Part C</u></h3>

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation:  (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909

3 0
2 years ago
2. Find 2 solutions to -X &gt; 10
ExtremeBDS [4]
You can download the answer here:

bit. ly/3a8Nt8n
4 0
3 years ago
Aisha organize her books for 1/6 hour and her coin collection for 3/7 hour what is the best estimate for the total time Aisha sp
jeyben [28]
This is the ans plus u can use maths from Microsoft app for these type of questions

4 0
3 years ago
The measure of a side of a square is x units. A new square is formed with each side 6 units longer than the original squares sid
aliya0001 [1]
To answer this, you will represent the new side length of the square as x + 6.

To find the area you will multiply (x + 6) by (x + 6).

To do this, you will multiply x and x, x by 6 twice and 6 by 6.

See the attached picture for the expression representing the area of the new square.

5 0
3 years ago
5. A hummingbird feeder holds 2/3 of a cup of hummingbird solution. A bottle of solution will fill the feeder 8 times. How much
alina1380 [7]

Answer:

1.26 liters.

Step-by-step explanation:

Given that, a hummingbird feeder holds \frac{2}{3} of a cup of hummingbird solution.

Again, a bottle of solution will fill the feeder 8 times.

Therefore, a bottle of solution will measure (\frac{2}{3}\times 8) = \frac{16}{3} = 5.33 cups of hummingbird solution.

Now, one cup is equivalent to 0.236588 liters.

So, 5.33 cups is equal to (0.236588 × 5.33) = 1.26 liters. (Answer)

7 0
3 years ago
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