Find the roots of the polynomial p(x) = x4 + 4x3 + 6x2 + 4x + 5=0, etc

[soneh]

Please guys I need help in the following question.

1. Find the roots of the polynomial p(x) = x⁴ + 4x³ + 6x² + 4x + 5=0 given that one of the roots is x = -i

2. Each of my 39 friends has either a dog, a cat or a rabbit. 24 of the have a dog, 17 have a cat and 16 have a rabbit. The number having both dog and cat is 1 more than the number having both cat and rabbit. There are 9 who have both dog and rabbit, while two of them have all three. How many of my friends have both rabbit and cat?

3.

Prove that the equation mx(x² + 2x + 3) = x² – 2x – 3 has exactly one real root if m = 1 and exactly 3 real roots if m= -2

 

[Deleted member 4993]

Please guys I need help in the following question.
1. Find the roots of the polynomial p(x) = x⁴ + 4x³ + 6x² + 4x + 5=0 given that one of the roots is x = -i
2. Each of my 39 friends has either a dog, a cat or a rabbit. 24 of the have a dog, 17 have a cat and 16 have a rabbit. The number having both dog and cat is 1 more than the number having both cat and rabbit. There are 9 who have both dog and rabbit, while two of them have all three. How many of my friends have both rabbit and cat?
3.

Prove that the equation mx(x² + 2x + 3) = x² – 2x – 3 has exactly one real root if m = 1 and exactly 3 real roots if m= -2

For 3, if m = 1 → what does the equation look like? Then factorize
and
For 3, if m = -2 → what does the equation look like? Then factorize

What are your thoughts?

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[stapel]

1. Find the roots of the polynomial p(x) = x⁴ + 4x³ + 6x² + 4x + 5=0 given that one of the roots is x = -i

If one root is x = -i, then what must be another root? Then what must be a factor? What is left, after you divide out this factor? How might the Quadratic Formula be brought to bear?

2. Each of my 39 friends has either a dog, a cat or a rabbit. 24 of the have a dog, 17 have a cat and 16 have a rabbit. The number having both dog and cat is 1 more than the number having both cat and rabbit. There are 9 who have both dog and rabbit, while two of them have all three. How many of my friends have both rabbit and cat?

What did you get when you set up the Venn diagram? (link)

3.

I hope the graphic isn't important, since of course nobody is going to try to hack your computer in order to locate it. :shock:

Prove that the equation mx(x² + 2x + 3) = x² – 2x – 3 has exactly one real root if m = 1 and exactly 3 real roots if m= -2

If m = 1, then what is the equation? What results do you obtain? If m = -2, then what is the equation? What results do you obtain?

Please be complete. Thank you!