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3 years ago

How to find the roots of a polynomial of degree 4.

Mathematics

1 answer:

german3 years ago

7 0

Answer:

In this case, the factor that comes out is x=−3, so you would divide by (x+3). Repeat until you've reduced to a quadratic, and then use the quadratic formula to find the irrational coefficients (if any). Simple factorisation solves your problem. Hence the 4 roots are x=12,x=−3,x=2i and x=−2i.

You might be interested in

The greatestcommonfactor of 8, 52

Nadusha1986 [10]

The GCF is the largest number that both will divide into. Eight is the larger of the two, but 52 is not divisible by 8. The next highest value is 4. 8÷4=2 and 52÷4=13. Therefore, the GCF is 4.

6 0

3 years ago

Your team wins 18 medals at a competition. The metals are gold, silver, and bronze in a ratio of 2:4:3. How many of each metal d

Anarel [89]

Answer

Find out the how many of each metal did your team win.

To prove

As given

Your team wins 18 medals at a competition.

The metals are gold, silver, and bronze in a ratio of 2:4:3.

Let us assume that x be the scalar multiple of the gold, silver and bronze medal.

Thus

Number of gold medal = 2x

Number of silver medal = 4x

Number of bronze medal = 3x

Than the equation becomes

2x + 4x + 3x = 18

9x = 18

$x = \frac{18}{9}$

x = 2

Number of gold medal = 2 × 2

= 4

Number of silver medal = 4 × 2

= 8

Number of bronze medal = 3 × 2

= 6

Therefore the number of gold medal are 4, silver medal are 8, bronze medal are 6.

3 0

3 years ago

Suppose R = {1,3,5,7,9,11,13,15,17} and D={3,6,9,12,15,18,21,24,27} r d

Free_Kalibri [48]

The intersection of sets R and D is give by the following set:

R ∩ D = {3, 9, 15}.

<h3>What is the missing information?</h3>

This problem is incomplete, but researching it on a search engine, we find that it asks the intersection of sets R and D.

<h3>What is the set that is the intersection of two sets?</h3>

The set that is the intersection of two sets is composed by the elements that belong to both sets.

For this problem, the sets are given as follows:

R = {1,3,5,7,9,11,13,15,17}.

D={3,6,9,12,15,18,21,24,27}

Hence the intersection is given by:

R ∩ D = {3, 9, 15}.

As the elements 3, 9 and 15 are the only ones that belong to both sets.

More can be learned about intersection of sets at brainly.com/question/11439924

#SPJ1

3 0

1 year ago

4/7 divided by 1 3/4

poizon [28]

Answer:

16/49

Step-by-step explanation:

4/7 ÷ 1 3/4

Convert 1 3/4 into an improper fraction

4/7 ÷ 7/4

Find the reciprocal of 7/4 and multiply

4/7 * 4/7

16/49

Hope this helps :)

7 0

3 years ago

Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

Feliz [49]

$f(x,y,z)=2z^2x+y^3$

$f$ has gradient

$\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k$

which at the point (-1, 4, 3) has a value of

$\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k$

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say $\vec u=15\,\vec\imath+25\,\vec\jmath$ , in which case we have

$\|\vec u\|=\sqrt{15^2+25^2}=5\sqrt{34}$

Then the derivative of $f$ at (-1, 4, 3) in the direction of $\vec u$ is

$D_{\vec u}f(-1,4,3)=\nabla f(-1,4,3)\cdot\dfrac{\vec u}{\|\vec u\|}=\boxed{\dfrac{294}{\sqrt{34}}}$

4 0

3 years ago