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2 years ago

Without using a calculator, determine the number of real zeros of the function

Mathematics

1 answer:

kumpel [21]2 years ago

3 0

The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

<h3>How to determine the number of real zeros?</h3>

The equation of the function is given as:

$f(x) = x^3 + 4x^2 + x - 6$

Expand the function

$f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6$

Reorder the terms

$f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6$

Factor the expression

$f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)$

Factor out x -1

$f(x) = (x^2 + 5x + 6)(x -1)$

Expand

$f(x) = (x^2 + 3x + 2x + 6)(x -1)$

Factorize

$f(x) = [x(x + 3) + 2(x + 3)](x - 1)$

Factor out x + 2

$f(x) = (x + 3)(x + 2)(x- 1)$

The function has been completely factored and it has 3 linear factors

Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

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Find the general solution of (x+3)y’=2y

gregori [183]

Answer:

$y=C(x+3)^2$

Step-by-step explanation:

We are given:

$\displaystyle (x+3)y^\prime=2y$

Separation of Variables:

$\displaystyle \frac{1}{y}\frac{dy}{dx}=\frac{2}{x+3}$

So:

$\displaystyle \frac{dy}{y}=\frac{2}{x+3} \, dx$

Integrate:

$\displaystyle \int\frac{dy}{y}=\int\frac{2}{x+3}\, dx$

Integrate:

$\displaystyle \ln|y|=2\ln|x+3|+C$

Raise both sides to e:

$|y|=e^{2\ln|x+3|+C}$

Simplify:

$|y|=(e^{\ln|x+3|})^2\cdot e^C$

So:

$|y|=C|x+3|^2$

Simplify:

$y=\pm C(x+3)^2=C(x+3)^2$

5 0

3 years ago

In rectangle ANGL, AN = 16 and AG = 34. Find the perimeter of ANGL.

Viktor [21]

In a rectangle, opposite sides are equal so you can multiply the side lengths by 2 and add them so 16(2)+34(2) and yu get 32+68. The perimeter is 100

8 0

3 years ago

Read 2 more answers

Marion Pelk worked 9 days in two weeks. He worked each day and was paid $7.1 an hour. What gross pay he earn for the two weeks?

Andrews [41]

Answer:

$1533.60 !

Step-by-step explanation:

$7.10 per hour needs to be times by 24 (to calculate the pay per day) = $170.40 then times that by 9 = $1533.60 (The pay for 9 days which is coincidently the pay per 2 weeks!

Job done! The answer is $1533.60!

[If I am wrong please message me and tell me]

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3 years ago

Can anyone help me please

Nady [450]

Yo sup??

since WY is the perpendicular bisector we can say

3x-5=2x+3

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Hope this helps

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3 years ago

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ElenaW [278]

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3 years ago