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Basile [38]
3 years ago
15

Find a polynomial function p of lowest​ degree, having rational​ coefficients, with the given zero. 5i

Mathematics
1 answer:
weqwewe [10]3 years ago
7 0
If we have one zero of +5i, we also have to have its conjugate which is -5i.  Therefore, the factors that we will FOIL to get that polynomial are (x+5i)(x-5i).  That distribution results in x^{2} -25 i^{2}.  I'm sure by now you know that i squared is equal to -1, so -25(-1) = 25.  So our polynomial is x^{2} +25=y
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Answer:

titutex=cos\alp,\alp∈[0:;π]

\displaystyle Then\; |x+\sqrt{1-x^2}|=\sqrt{2}(2x^2-1)\Leftright |cos\alp +sin\alp |=\sqrt{2}(2cos^2\alp -1)Then∣x+

1−x

2

∣=

2

(2x

2

−1)\Leftright∣cos\alp+sin\alp∣=

2

(2cos

2

\alp−1)

\displaystyle |\N {\sqrt{2}}cos(\alp-\frac{\pi}{4})|=\N {\sqrt{2}}cos(2\alp )\Right \alp\in[0\: ;\: \frac{\pi}{4}]\cup [\frac{3\pi}{4}\: ;\: \pi]∣N

2

cos(\alp−

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cos(2\alp)\Right\alp∈[0;

4

π

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4

3π

;π]

1) \displaystyle \alp \in [0\: ;\: \frac{\pi}{4}]\alp∈[0;

4

π

]

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π

)=cos(2\alp)…

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4

3π

;π]

\displaystyle -cos(\alp -\frac{\pi}{4})=cos(2\alp )\dots−cos(\alp−

4

π

)=cos(2\alp)…

1

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