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VARVARA [1.3K]
3 years ago
5

Remainder of 8529 divided by 42

Mathematics
1 answer:
OverLord2011 [107]3 years ago
4 0
When a number is not completely divisible by a second number, there is an excess which is known as the remainder. In this case, 8529 divided by 42 yields the answer of 203.071. We can calculate the remainder by multiplying 203 by 42 and subtracting the answer from 8529. In this case the remainder is 3. 
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Find the polynomial of lowest degree with only real coefficients and having the given zeros. -7i and square root of 2
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Answer:

x³ - (√2)x² + 49x - 49√2

Step-by-step explanation:

If one root is -7i, another root must be 7i.  You can't just have one root with i.  The other roos is √2, so there are 3 roots.  

x = -7i       is one root,

   (x + 7i) = 0    is the factor

x = 7i       is one root

  (x - 7i) = 0     is the factor

x = √2      is one root

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So the factors are...

(x + 7i)(x - 7i)(x - √2) = 0

Multiply these out to find the polynomial...

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Which simplifies to

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(x² + 49)(x - √2) = 0

Now foil this out...

 x²(x) - x²(-√2) + 49(x) + 49(-√2) = 0

     x³ + (√2)x² + 49x - 49√2

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