2 years ago

What operation is the opposite of multiplication

Mathematics

1 answer:

tatiyna2 years ago

4 0

What is the opposite operation of multiplication
the division

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Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities inclu

Softa [21]

Answer-

The polynomial function is,

$y=x^4-10x^3+38x^2-64x+40$

Solution-

The zeros of the polynomial are 2 and (3+i). Root 2 has multiplicity of 2 and (3+i) has multiplicity of 1

The general form of the equation will be,

$\Rightarrow y=(x-(2))^2(x-(3+i))(x-(3-i))$ ( ∵ (3-i) is the conjugate of (3+i) )

$\Rightarrow y=(x-2)^2(x-3-i)(x-3+i)$

$\Rightarrow y=(x^2-4x+4)((x-3)-i)((x-3)+i)$

$\Rightarrow y=(x^2-4x+4)((x-3)^2-i^2)$

$\Rightarrow y=(x^2-4x+4)((x^2-6x+9)+1)$

$\Rightarrow y=(x^2-4x+4)(x^2-6x+10)$

$\Rightarrow y=x^2x^2-6x^2x+10x^2-4x^2x+4\cdot \:6xx-4\cdot \:10x+4x^2-4\cdot \:6x+4\cdot \:10$

$\Rightarrow y=x^4-10x^3+14x^2+24x^2-40x-24x+40$

$\Rightarrow y=x^4-10x^3+38x^2-64x+40$

Therefore, this is the required polynomial function.

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Answer:

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Step-by-step explanation:

The A and the .

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