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2 years ago

What are the zeros of the polynomial function?

Mathematics

1 answer:

umka21 [38]2 years ago

8 0

X+14=0
X-5=0

The zeroes are. -14 and 5

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The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

7 0

2 years ago

PLS HELP WILL GIVE BRANLIEST

nalin [4]

Answer:

Step-by-step explanation:

hope this helped. I am in algebra two so you can trust my answer. happy holidays and stay safe

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2 years ago

The walls of a farm silo form a hexagonal prism as shown. What is the volume of the silo?

Valentin [98]

I think this is what you meant you meant silo or Solid if you meat solid the answer is there in the picture

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3 years ago

Can anyone find the area of this triangle ?

Alexxx [7]

12Sqrt(3)

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3 years ago

For r=2+3sintheta find dy/dx and the slope of the tangent line to the curve

brilliants [131]

F(x)=2+3sin(theta)
f'(x)=3cos(theta)

To find the slope you need the value of theta. The general formula is:

y-f(xo)=f'(xo)-(x-xo)

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3 years ago