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fgiga [73]
3 years ago
8

Find all the zeros of

3%7D%20%20-%20%20%7B4x%7D%5E%7B2%7D%20%20%2B%207x%20-%202" id="TexFormula1" title="f(x) = {6x}^{4} - {7x}^{3} - {4x}^{2} + 7x - 2" alt="f(x) = {6x}^{4} - {7x}^{3} - {4x}^{2} + 7x - 2" align="absmiddle" class="latex-formula">
​

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
5 0

Answer:

  {-1, 1/2, 2/3, 1}

Step-by-step explanation:

I find a graphing calculator to be a most useful tool for problems like this. (See attached.)

_____

First of all, observe that the constant is -2, so 0 is not a zero.

It is often useful to look at the sum of coefficients. Here, that is 0, indicating 1 is a zero.

You can divide that out, or simply continue by looking at the sum of coefficients with odd-degree terms negated. Then you have 6 +7 -4 -7 -2 = 0, indicating -1 is also a zero.

__

At this point, it can be useful to divide out the factors you know. The synthetic division tableaus attached show that work. First is division by (x+1), then by (x -1).

The result of doing that is the quadratic ...

  6x^2 -7x +2 = 0

This can be factored ...

  (6x^2 -3x) -(4x -2) = 0 . . . . . . rewrite -7x and group term pairs

  3x(2x -1) -2(2x -1) = 0 . . . . . . . factor each pair

  (3x -2)(2x -1) = 0 . . . . . . the factorization of the remaining quadratic

The zeros of this are the values of x that make the factors zero: 2/3 and 1/2.

The zeros of the given function f(x) are x ∈ {-1, 1/2, 2/3, 1}.

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What is x? -2.5x- 2=18​
snow_tiger [21]

Answer:

x = -8

Step-by-step explanation:

-2.5x - 2 = 18.

Add 2 to both sides.

-2.5x = 20.

Divide both sides by -2.5.

x = -8

3 0
3 years ago
QR is the midsection of triangle GHJ, what is the length of QR?
Xelga [282]

Answer:

Step-by-step explanation:

QR = 27 ÷ 2 = 13.5

6 0
3 years ago
4. Gloria the grasshopper is working on her hops.
aivan3 [116]

The path that Gloria follows when she jumped is a path of parabola.

The equation of the parabola  that describes the path of her jump is \mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

The given parameters are:

\mathbf{Height = 20}

\mathbf{Length = 28}

<em>Assume she starts from the origin (0,0)</em>

The midpoint would be:

\mathbf{Mid = \frac 12 \times Length}

\mathbf{Mid = \frac 12 \times 28}

\mathbf{Mid = 14}

So, the vertex of the parabola is:

\mathbf{Vertex = (Mid,Height)}

Express properly as:

\mathbf{(h,k) = (14,20)}

A point on the graph would be:

\mathbf{(x,y) = (28,0)}

The equation of a parabola is calculated using:

\mathbf{y = a(x - h)^2 + k}

Substitute \mathbf{(h,k) = (14,20)} in \mathbf{y = a(x - h)^2 + k}

\mathbf{y = a(x - 14)^2 + 20}

Substitute \mathbf{(x,y) = (28,0)} in \mathbf{y = a(x - 14)^2 + 20}

\mathbf{0 = a(28 - 14)^2 + 20}

\mathbf{0 = a(14)^2 + 20}

Collect like terms

\mathbf{a(14)^2 =- 20}

Solve for a

\mathbf{a =- \frac{20}{14^2}}

\mathbf{a =- \frac{20}{196}}

Simplify

\mathbf{a =- \frac{5}{49}}

Substitute \mathbf{a =- \frac{5}{49}} in \mathbf{y = a(x - 14)^2 + 20}

\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

Hence, the equation of the parabola  that describes the path of her jump is \mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

See attachment for the graph

Read more about equations of parabola at:

brainly.com/question/4074088

7 0
2 years ago
10t = 90 <br><br> i seriously dont know what to put to make it longer anymore bruv
kondor19780726 [428]

Answer:t= 9

Step-by-step explanation: 10t =90

                                           divide 10 on both sides

                                            so 10t /10 and 90/10

                                             which means t=9

8 0
3 years ago
Read 2 more answers
Someone please help me out with number 8 and 9 and 10
Ket [755]

Answer:

9. 0.0539 Liters

10. 216 quarts

Step-by-step explanation:

I dont know the answer to 8 but i do for 9 and 10!

plz drop a brainliest.

8 0
3 years ago
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