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Dmitriy789 [7]
3 years ago
14

Write an equation in standard form of the line that passes through (3, 1) and has a y intercept of -2

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
3 0

Step-by-step explanation:

First of all, use substitution to find slope

(1) = m(3) - 2

3 = m3

m = 1

With both the slope and y int, you can write it in y int form

y = 1x - 2

Convert that to standard form

-x + y = -2

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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

    (x - √2) = 0   is the factor

So the factors are...

(x + 7i)(x - 7i)(x - √2) = 0

Multiply these out to find the polynomial...

(x + 7i)(x - 7i) =  x² + 7i - 7i - 49i²

Which simplifies to

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Now foil this out...

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

     x³ + (√2)x² + 49x - 49√2

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