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Finger [1]
2 years ago
15

PLEASEEE HELPPPP IM BEGGIN U

Mathematics
1 answer:
Anna71 [15]2 years ago
6 0

Answer:

  a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)

  b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.

  c, d) See attached

Step-by-step explanation:

Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.

Synthetic division is essentially polynomial long division with some modifications:

  • the variables are omitted ("place value" is used instead)
  • the constant in the divisor is <em>negated</em> so its product with the partial quotient can be <em>added</em> to obtain the new dividend
  • the divisor binomial is assumed to have a leading coefficient of 1.

__

<h3>a) </h3>

The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.

When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.

Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.

The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.

__

<h3>b)</h3>

The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.

Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.

__

<h3>c)</h3>

The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)

Maybe this is the table you want:

  \begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}

__

<h3>d)</h3>

The second attachment shows synthetic division by the factor (x+4).

_____

<em>Additional comment</em>

The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.

The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.

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Solution:

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and each pond of almonds cost $y.

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3 0
3 years ago
Use algebra to find the point at which the line h(x)=−(3/5)x+(7/5) intersects the line k(x)=(−8/3)x+(404/45).
Inga [223]

Answer: the point (3.667, 0.8)

Step-by-step explanation:

We want to find the point at which the lines:

h(x) = -(3/5)*x + (7/5)

and

k(x) = (-8/3)*x + (404/45)

If the lines intersect, then we must have:

h(x) = k(x)

if we write the functions we get:

-(3/5)*x + (7/5) = (-8/3)*x + (404/45)

Now we need to solve this for x.

-(3/5)*x + (8/3)*x = (404/45) - (7/5)

(8/3 - 3/5)*x = 404/45 - 63/45 = 341/45

(40/15 - 9/15)*x = 341/45

(31/15)*x = 341/45

x = (341/45)*(15/31) = 3.667

Now we can input this value of x in the functions to get the output.

h(3.667) = -(3/5)*3.667 + 7/5 = -0.8

Then the point where our points intersect is the point (3.667, 0.8)

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2 years ago
Lillian and Isabella went shopping for school supplies. Lillian found her favorite notebook on sale so she bought three of the e
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Answer:

Each girl had $7.50 when they arrived.

Step-by-step explanation:

We have to figure out what c (cost of each notebook) is first before we find out how much money each girl had. We also know they have the same money, so both sides are connected. The equation should be: 3x = x + 5.

3x = x + 5

<em>First, subtract x from both sides. This cancels out the addition by x.</em>

3x - x = 5

<em>Now, subtract x from 3x. This equals 2x.</em>

2x = 5

<em>To cancel out the multiplication by 2, divide both sides by 2.</em>

x = 5/2

<em>Lastly, divide 5 by 2 to get 2.5.</em>

x = 2.5

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3(2.5) = 2.5 + 5

<em>First, multiply 3 by 2.5 to get 7.5.</em>

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<em>Add 2.5 to 5 to get 7.5.</em>

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3 years ago
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AysviL [449]
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ivann1987 [24]

Answer:

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Step-by-step explanation:

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3 years ago
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