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Aleonysh [2.5K]
4 years ago
13

Consider the function f(x)=3x^3-5x^2-88x+60-5 is a root of f(x). Find all of the roots of f(x)

Mathematics
1 answer:
Tom [10]4 years ago
8 0
If -5 is a root then f(x) is divisible by x + 5

The quotient from this division is 3x^2 -20x +12
Factoring this:-

= 3x^2 - 18x - 2x + 12
= 3x(x - 6) - 2(x - 6)
= (3x - 2)(x - 6)
So 2 more roots are 2/3 and 6
All the roots are -5 , 2/3 and 6.  Answer
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3√x -2/x^2<br><br>please show step by step of differentiation before combining the terms. ​
EastWind [94]

Answer:

Step-by-step explanation:

Before we differentiate, let us assign a variable to the function. Let y be equal to the function i.e let y = 3√x -2/x²

In differentiation if y = ax^{n}, then \frac{dy}{dx} = nax^{n-1} where n is a constant and dy/dx means we are differentiating the function y with respect to x.

Applying the formula o the question given;

y= 3\sqrt{x}  -2/x^2\\y = 3{x}^\frac{1}{2}  - 2x^{-2} \\\\

On differentiating the resulting function;

\frac{dy}{dx} = \frac{1}{2}*3x^{\frac{1}{2}-1 }   - (-2)x^{-2-1} \\\\\frac{dy}{dx} = \frac{1}{2}*3x^{-\frac{1}{2}} + 2x^{-3}\\ \\\frac{dy}{dx} = \frac{1}{2}*{\frac{3}{x^{\frac{1}{2} } }} + \frac{2}{x^{3} } \\\\\frac{dy}{dx} = {\frac{3}{2x^{\frac{1}{2} } }} + \frac{2}{x^{3} }\\\\\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }

To combine the terms, we will add up by finding their LCM.

\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }\\\frac{dy}{dx}  = \frac{3x^3+4\sqrt{x} }{2x^{3} \sqrt{x}}

3 0
4 years ago
You can buy 20 ounces of cereal for $4.40 or 16 ounces of the same brand for $3.68. Which is the better buy?
Natalka [10]
The answer to your Q the better one is the 16 ounces of cereal because it is the least
3 0
4 years ago
Resolver el siguiente sistema de ecuación:
snow_tiger [21]

Answer:

x=-1\\y=4

Step-by-step explanation:

\frac{5x+2y}{3}=1

\frac{2x+y}{2}=1

Vamos a utilizar el método de sustitución. Vamos a despejar la segunda ecuación por alguna de las variables. Elegiré la y porque esta sola.

\frac{2x+y}{2}=1

Vamos a empezar por eliminar ese 2 del denominador. Para hacer esto, multiplicamos por 2 ambos lados de la ecuación.

2x+y=1*2

2x+y=2

Como vamos a despejar la y, restamos 2x en ambos lados.

y=2-2x

Listo.

------------------------------------------------------------------------

Procedemos a reemplazar el valor de y en la primera ecuación.

\frac{5x+2y}{3}=1

\frac{5x+2(2-2x)}{3}=1

\frac{5x+4-4x}{3} =1

Procedemos a operar términos semejantes.

\frac{x+4}{3} =1

Nos deshacemos del 3 multiplicando.

x+4=1*3\\x+4=3

Restamos 4

x=3-4\\x=-1

-----------------------------------------------------------------------------

Una vez encontrado el valor de x, procedemos a reemplazar en cualquier ecuación para encontrar el valor de y. Usaré la segunda ecuación.

\frac{2x+y}{2}=1

\frac{2(-1)+y}{2}=1

Procedemos a resolver;

\frac{-2+y}{2} =1

Multiplicamos por 2.

-2+y=1*2

-2+y=2

Sumamos 2

y=2+2\\y=4

-------------------------------------------------------------------------------

Para comprobar que los valores son correctos, reemplazamos ambos valores en cualquier ecuación y el resultado debe ser igual.

Usaré la primera.

\frac{5x+2y}{3} =1

\frac{5(-1)+2(4)}{3} =1

Resolvemos;

\frac{-5+8}{3} =1

\frac{3}{3}=1

1=1

6 0
4 years ago
what is the definition of value? i need that answer. if your Answered this question you gonna get 49 point!!!!!!!!!!!!!!!!!!!!!!
timurjin [86]

Answer:

In math, value can either refer to the result of a calculation or a variable or constant

5 0
4 years ago
Read 2 more answers
4x+2y=5 , 2x-3y=13 pair of equations to two decimal places of accuracy. ​
slavikrds [6]

Answer:

x = 2.56, y = -2.63

Step-by-step explanation:

I first multiplied the second equation by two, getting

4x-6y = 26

I then subtracted the equations

 4x+2y = 5

- 4x-6y = 26

--------------------

      8y = -21

y = -2.63

with y solved, I plugged it into the second equation to get x:

2x-3(-2.63) = 13

2x+ 7.89 = 13

2x = 5.11

x = 2.56

I hope this helped! ;D

6 0
3 years ago
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