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2 years ago

(x2 - 2)(x + 1) = (x^)(5x)+(x2)() + (-2)(5x) + (-2)(1) is an example of:

Mathematics

1 answer:

OLga [1]2 years ago

3 0

Answer:

Step-by-step explanation:

It is complex conjunction

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Find all the zeros of the equation x^4-6x^2-7x-6=0

rusak2 [61]

Answer:

The zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Step-by-step explanation:

We have been given the equation x^4-6x^2-7x-6=0

Use rational root theorem, we have

$a_0=6,\:\quad a_n=1$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}$

$-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2$

$=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\$

$=x^3-2x^2-2x-3$

Again factor using the rational root test, we get

$=\left(x+2\right)\left(x-3\right)\left(x^2+x+1\right)$

Using the zero product rule, we have

$x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Therefore, the zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

4 0

2 years ago

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25% of Mr. Foster's class chose an amber background for their school picture. If 6 students chose an amber background, how many

Lelu [443]

Answer:

<h2>24 students</h2>

Step-by-step explanation:

25% of a hundred is one-fourth and because there are six students in a fourth of the whole we are multiplying four and six. 6x 4 is 24.

5 0

2 years ago

Stephen has a dog that weigths 5 times as much as lan's dog.The total weigths of both dogs is 72 pounds.How much does Stephens d

vesna_86 [32]

Answer: Stephens dog weighs 60 pounds

Step-by-step explanation:

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2 years ago

Y = - 2/3x + 2 in standard form

Lesechka [4]

Answer:

2x + 3y = 6

Step-by-step explanation:

2x + 3y = 6

-2x. -2x

3y/3 = -2x + 6/3

Y = -2/3x + 2

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2 years ago

Is it true that x= -5 ? -2(-4x-1)-x+3=−30 Justify your answer.

grandymaker [24]

Answer:

Step-by-step explanation:

here you go mate

step 1

-2(-4x-1)-x+3=−30 equation/Question

step 2

-2(-4x-1)-x+3=−30 distribute

7x+5=-30

step 3

7x+5=-30 subtract 5

7x=-35

step 4

$\frac{7x}{7} =\frac{-35}{7}$ divide

answer

x=-5

6 0

2 years ago

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