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3 years ago

If 2 - 3i is a solution to the equation x3 - 3x2 + 9x + 13 = 0, what are the other roots of the equation?

1 answer:

4 0

The complex solutions come in pairs and the only difference between them is the sign between the real and imaginary part, so one of the other two solutions is $2+3i$ . The third solution can be easily found using the rational root theorem, and it's equal to -1.

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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

Read 2 more answers

1.2x-4y=28 solve for y

Gnesinka [82]

2x -4y= 28
⇒ -4y= 28 -2x
⇒ y= (28 -2x)/ (-4)
⇒ y= 28/(-4) -(2x)/ (-4)
⇒ y= -7 + 1/2x

The final answer is y= -7 + 1/2x~

4 0

2 years ago

HURRY PLEASE HELP ME? <br> WiLL GIvE brainliest.

solniwko [45]

Subtitute the pair (3,28) to x and y, if the result in right side is -8, then the pair is a solution to the equation

2x - y/2
= 2(3) - 28/2
= 6 - 14
= -8

The result is -8, so the pair (3,28) is a solution

3 0

2 years ago

Earning an A in algebra this semester is an example of:

Aleksandr [31]

Answer:

Step-by-step explanation:

A semester is about 1/2 of the school year which is 4 1/2 or 5 months, its not instant because its 5 months long its not short term commitment because you will have to work with it, and its not a short term goal because 5 months is quite a while in my opinion.

plz give brainliest

7 0

2 years ago

Read 2 more answers

Ronald is making hats and scarves for charity. He has enough yarn to make 5 hats and 8 scarves. Takes him 12 hrs to knit a hat,

kari74 [83]

Constraints are simply the subjects of an objective function.

The inequality that represents the constraint is: $12x + 6y \le 20$