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Novosadov [1.4K]

3 years ago

7

15 Points!

1 answer:

Virty [35]3 years ago

6 0

$5; -3; -1 -2i$
<span>In polynomials we have not of an imaginary unit (i), therefore we have the fourth zeros -1-2i.</span>

$f(x)=(x-5)(x+3)\left[x-(-1-2i)\right]\left[x-(-1+2i)\right]\\\\=(x^2+3x-5x-15)[x^2-x(-1+2i)-x(-1-2i)+(-1)^2-(2i)^2]\\\\=(x^2-2x-15)(x^2+x-2i+x+2i+1+4)\\\\=(x^2-2x-15)(x^2+2x+5)\\\\=x^4+2x^3+5x^2-2x^3-4x^2-10x-15x^2-30x-75\\\\=x^4-14x^2-40x-75$

Answer: B)

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Find the smallest positive integer k such that 3240/k is a square number

sashaice [31]

Answer:

10

Step-by-step explanation:

First, factorize the number 3,240:

$3,240=2\cdot 1,620=2\cdot 2\cdot 810=2\cdot 2\cdot 2\cdot 405=2\cdot 2\cdot 2\cdot 2\cdot 5\cdot 81=2^3\cdot 5\cdot 9^2$

So,

$3,240=2^2 \cdot 2\cdot 5\cdot 9^2=18^2\cdot 10$

Now consider the fraction

$\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{k}$

If k = 10, then

$\dfrac{3,240}{k}=\dfrac{18^2\cdot 10}{10}=18^2$

is a square number.

For all k < 10, the fraction tex]\dfrac{3,240}{k}[/tex] is not a square number (this follows from factorization).

Or you can simply check the values of the fraction for all k < 10:

k = 1, $\dfrac{3,240}{1}=3,240$ is not a square number;
k = 2, $\dfrac{3,240}{2}=1,620$ is not a square number;
k = 3, $\dfrac{3,240}{3}=1,080$ is not a square number;
k = 4, $\dfrac{3,240}{4}=810$ is not a square number;
k = 5, $\dfrac{3,240}{5}=648$ is not a square number;
k = 6, $\dfrac{3,240}{6}=540$ is not a square number;
k = 7, $\dfrac{3,240}{7}$ is not a square number;
k = 8, $\dfrac{3,240}{8}=405$ is not a square number;
k = 9, $\dfrac{3,240}{9}=360$ is not a square number.

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jolli1 [7]

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4vir4ik [10]

B.

Hope this helps!!!

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