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leva [86]
3 years ago
12

Write the expression of polynomial a given the roots:

Mathematics
2 answers:
Liono4ka [1.6K]3 years ago
4 0

Answer:

So it looks like the given zeros are 2i and -3. We have to work backwards.

x = -3 and x = 2i

For -3, we know that out factored form before would have been x + 3

For 2i, that means we took the square root of negative number because it is imaginary. So that means out factored for x2 + 4

So if we put these together:

(x2 + 4)(x + 3) = x3 + 3x2 + 4x + 12

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Step-by-step explanation:

Travka [436]3 years ago
3 0

Answer:

x³ - 3x² + 4x -12 = 0

Step-by-step explanation:

(x-2i)(x+2i)(x-3) = 0

(x² - 4*(√-1)²)(x-3) = 0

(x² + 4) ( x - 3) = 0

x³ - 3x² + 4x -12 = 0

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1) Inverse function: f^{-1}(x)=g(x)=\frac{x+4}{3}

2) f(1) = -1, g(-1) = 1

3) f(g(x))=g(f(x))=x

Step-by-step explanation:

1)

In this first method, we want to find the inverse function of f(x).

The original function is:

f(x) = 3x-4

We rewrite it as

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And dividing by 3 on both sides:

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which is identical to g(x):

g(x)=\frac{x+4}{3}

2)

In this second method, we want to use the output of one function as input to the other function, and show that the output value is equal to the imput value.

We start using the function

f(x)=3x-4

We choose x=1. We find:

f(1)=3(1)-4=3-4=-1

Now we use this output value as input in the function

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Substituting x=-1,

g(-1)=\frac{-1+4}{3}=\frac{3}{3}=1

So, the final output value (1) is equal to the input value (1).

3)

Here we want to verify that the two are inverse functions by showing that

f(g(x))=x

We have

f(x)=3x-4\\g(x)=\frac{x+4}{3}

Substituting g(x) into f(x),

f(g(x))=3g(x)-4 = 3(\frac{x+4}{3})-4=(x+4)-4=x

Viceversa, we want to show that

g(f(x))=x

Substituting g(x) into f(x), we get

g(f(x))=\frac{f(x)+4}{3}=\frac{(3x-4)+4}{3}=\frac{3x-4+4}{3}=\frac{3x}{3}=x

So, the two functions are one the inverse of the other.

Learn more about inverse functions:

brainly.com/question/1632445

brainly.com/question/2456302

brainly.com/question/3225044

#LearnwithBrainly

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