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3 years ago

Consider the fuction f(x)=x^4-3x^3-7x^2+15x+18

Mathematics

1 answer:

Andreyy893 years ago

5 0

When the equation is in the 4th degree, it is called a quartic equation. Solving the roots of a quartic solution is very tedious and lengthy. It could get messy because you would use other variables. If you want to know how, I hope this link could help you: http://mathforum.org/dr.math/faq/faq.cubic.equations.html

I would still give answers but these are determined with the help of tools like scientific calculator and MS Excel.

Part A. This question is very generic. There are many ways of finding the roots. Actually, part b, c and d are all solutions of this section.

Part B. This is how synthetic division works. The divisor is x-3=0 or x=3. Place it on the left side with a corner barrier. Then, place all the coefficients of the quartic equation in order on the right side. This is for the first row. Then, bring down the first coefficient 1 under the horizontal bar. Multiply 1 to the 3 on the left side. The product is 3 which placed under the second coefficient. When you add them, the sum is 0. Multiply this again with 3 on the left side and place this under the next coefficient. The pattern goes on and on.

3| 1 -3 -7 15 18
3 0 -21 -18
----------------------------------
1 0 -7 -6 0

When the last term is 0, it means that there is no remainder. Thus, x-3 is a factor.

Part C. It is quite challenging to factor a quartic equation. As previously mentioned, it can be messy. Just see the link to see the step-by-step procedure. Another alternative to this is by graphical under letter d.

Part D. Just assign values to x, substitute to the equation to get y. Then, plot x against y. The graph would look like that in the picture. The x-intercepts are the roots of the equation. From the picture, we can see that they are x=-1, x=-2 and x=3. The other root is a complex or imaginary.

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. All the students in SS3 of a named school take either Mathematics (M), or Physics (P) or Chemistry (C). 40 take Mathematics, 4

aivan3 [116]

Answer:

(a) = 13

(b) = 8

Step-by-step explanation:

Addition theorems on sets are

Theorem 1 :

n(AuB) = n(A) + n(B) - n(AnB)

Theorem 2 :

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

Total number of students in the school is not given

so let there are 60 students in the school

using theorem 2

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

60 = 40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)

60 +73 -120 = n(AnBnC)

13 = n(AnBnC)

therefore, there are total 13 students who take all three subjects

Number of students who had taken only Mathematics =
n(A) - n(AnB) - n(AnC) + n(AnBnC)

40 - 20 - 25 + 13

53 - 45 = 8 students

Number of students who had taken only Physics =

n(B) - n(BnA) - n(BnC) + n(AnBnC)

42 - 20 - 28 + 13

53 - 48 = 5 students

learn more about sets and vein diagrams at

brainly.com/question/2332158

#SPJ10

4 0

2 years ago

Is x^-3-5y^-2 a polynomial

KiRa [710]

Answer:

Yes, it is.

Step-by-step explanation:

A polynomial is a mathematical expression containing two or more terms.

For example, a+b is a polynomial. 2a-23b+c is also a polynomial.

Hope this helps :)

8 0

3 years ago

Read 2 more answers

Use the figure to complete each statement. a. m

erica [24]

To answer this u need to attach an image or type out the whole thing

4 0

4 years ago

Luis scored 22 out of 49 shots. How many would he be expected to score in 100 shots

FromTheMoon [43]

Answer:

Step-by-step explanation:

first subtract 22 from 49 then you would get 27 so you would just subtract 27 from 100.

6 0

3 years ago

If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams

Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

$N=N_0e^{-\lambda t}$

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

$\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34$ , t= 10

$N=N_0e^{-\lambda t}$

$\Rightarrow \frac {N}{N_0}=e^{-\lambda t}$

$\Rightarrow \frac34 =e^{-\lambda .10}$

Taking ln both sides

$\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|$

$\Rightarrow ln|\frac34|=-10\lambda$

$\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}$

Now , N₀= 512 grams, N= 121.5 grams, t=?

$N=N_0e^{-\lambda t}$

$\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}$

$\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}$

$\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|$

$\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}$

$\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}$

$\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}$

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

8 0

4 years ago