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3 years ago

How many solutions over the complex number system does this polynomial have

Mathematics

2 answers:

Oksi-84 [34.3K]3 years ago

6 0

For this case we have the following polynomial.
We note that the polynomial graph cuts only the vertical axis at one point.
The graph has no other cut points on the x axis
Therefore, the polynomial has:
6 complex solutions
0 real solution
Answer:
6 complex solutions
See attached image

Readme [11.4K]3 years ago

6 0

Answer:

6 complex solutions

Step-by-step explanation:

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Likurg_2 [28]

$x = 2.857$

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}$

$6x - 9 - 2(1 - x) = x + 9 \\ ⇢ 6x - 9 - 2 + 2x = x + 9 \\ ⇢ 8x - x = 9 + 11 \\ ⇢ 7x = 20 \\ ⇢ x = \frac{20}{7} \\ ⇢ x = 2.857$

${ \bf{ \underbrace{To\:verify:}}}$

$6 \times 2.857 - 9 - 2(1 - 2.857) = 2.857 + 9 \\ ➪ \: 17.142 - 9 - 2 \times( - 1.857) = 11.857 \\➪ \: 8.142 + 3.714 = 11.857 \\➪ \: 11.856 = 11.857 \\ ➪ \: 11.86 = 11.86 \\ ➪ L.H.S.=R. H. S$

Hence verified.

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