Write a polynomial equation of degree 4 in standard form that has the solutions i, −i, 1, −1.
1 answer:
Answer:
x⁴ + 2 x² + 1
Step-by-step explanation:
given solution of the polynomial
i, −i, 1, −1.
equation of the polynomial will be equal to
=(x - i)(x + i)(x - 1)(x + 1)
= (x² + i x - i x - i²)(x² + x - x + 1)
=(x² - (-1))(x² + 1 )
= (x² + 1)(x² + 1)
= x⁴ + x² + x² + 1
= x⁴ + 2 x² + 1
hence, the required polynomial equation is x⁴ + 2 x² + 1
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
1. Add the x
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Hope this helps!
Answer:
2(x+4)
Step-by-step explanation:
common denominator is 2
Check the picture below.
notice the alternate interior angles in the picture.
![\bf tan(68^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{x}}\implies x=\cfrac{1.5}{tan(68^o)}\implies x\approx 0.61 \\\\[-0.35em] ~\dotfill\\\\ tan(56^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{w}}\implies w=\cfrac{1.5}{tan(56^o)}\implies w\approx 1.01 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{width of the crater}}{x+w\implies 1.62}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20tan%2868%5Eo%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B1.5%7D%7D%7B%5Cstackrel%7Badjacent%7D%7Bx%7D%7D%5Cimplies%20x%3D%5Ccfrac%7B1.5%7D%7Btan%2868%5Eo%29%7D%5Cimplies%20x%5Capprox%200.61%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20tan%2856%5Eo%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B1.5%7D%7D%7B%5Cstackrel%7Badjacent%7D%7Bw%7D%7D%5Cimplies%20w%3D%5Ccfrac%7B1.5%7D%7Btan%2856%5Eo%29%7D%5Cimplies%20w%5Capprox%201.01%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7B%5Ctextit%7Bwidth%20of%20the%20crater%7D%7D%7Bx%2Bw%5Cimplies%201.62%7D~%5Chfill)
6,200×(((1+0.06÷2)^(2×5)
−1)÷(0.06÷2))
=71,076.05
