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1 year ago

Write as a product of two polynomials. 2(3-b)+5(b-3)^2

Mathematics

1 answer:

viktelen [127]1 year ago

4 0

Answer:

$5b^{2}-32b+51$

Step-by-step explanation:

$2(3-b)+5(b-3)^{2}$

$=6-2b+5b^{2}-30b+45$

$=5b^{2}-32b+51$

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Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

$x^4-(3m+2)x^2+m^2=0$

$x^4+0x^3-(3m+2)x^2+0x+m^2=0$

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

$a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}$

$=\frac{0}{1}=0$

$\implies a=0----(1)$

$(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}$

$=\frac{-3m-2}{1}$

$3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2$

$-10b^2=-3m-2$

$\implies b^2=\frac{3m+2}{10}-----(2)$

$(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2$

$9b^4=m^2$

$9(\frac{3m+2}{10})^2=m^2$

$9(\frac{9m^2+4+12m}{100})=m^2$

$81m^2+36+108m=100m^2$

$-19m^2+108m+36=0$

$19m^2-108m-36=0$

$19m^2-114m+6m-36=0$

$19m(m-6)+6(m-6)=0$

$(19m+6)(m-6)=0$

$\implies m=-\frac{6}{19}\text{ or }m=6$

But m > 0,

Hence, the value of m is 6.

4 0

2 years ago

Suppose the line of best fit is being found for some points that have an r-value of 0.769. If the standard deviation of the x-co

jeyben [28]

r value i.e Correlation between x value and y value = 0.769

$A_{x}$ =Standard deviation of the x-coordinate = 5.508

$A_{y}$ =Standard deviation of the y-coordinate = ?=k

Slope of line is given by formula

If slope of line is m, then

m = $r\times \frac{ A_{x}}{A _{y}}$

m= $0.769 \times \frac{k}{5.508}$

Substitute the value of k, i.e Standard deviation of the y-coordinate and then you can get the slope of line to three decimal places.

7 0

2 years ago

For the following geometric sequence find the explicit formula {1,-3,9,...}

Zarrin [17]

The first term of this series (a+1) is 1 and the common ratio (r) is -3.

Thus, the explicit formula is a_n = 1*(-3)^(n-1).

Must check this! suppose we try to calculate the 3rd term. Then n = 3.

a_3 = 1*(-3)^(3-1) = (-3)^2 = 9. This is correct.

3 0

2 years ago

Read 2 more answers

Fill in the question mark ?5

timurjin [86]

I don't really understand your question , can you rephrase it ?

Do you mean ?5x7 = 455 ?
because then it would be :
455 divided by 7 which equals 65 :)

7 0

2 years ago

Please answer this!!! No links !!!

stealth61 [152]

My work for your question

8 0

2 years ago