सांशलेषिक विभाजन विधि का प्रयोग करके यह दर्शाइए कि 2, समीकरण का एक सरल मूल है।
दिया गया बहुपद p(x) = x⁴ − 2x³ + x² − x − 2 सांश्लेषिक विभाजन द्वारा x = 2 की जाँच करते __________ _____ ________ ___ _________ _______ _________ __________ ___.
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______ ______ ________ ________ _____ _______ _________ _________ _________.
________ ___ _________ _________ ____ ____ _____ ________ _________ _______ __________ __________.
________ ______ ________ _____ ___ ______ ________.
__________ _____ ________ ________ ________ __________ ______ ____ ______ _________.
___ ______ ___ _________ ________ __________ _____ ___ __________ ______ ________ ____.
_________ _______ ________ ________ __________ ________ ___ ____ _________ ____ ___.
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__________ __________ __________ _____ ______ _______.
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Find the approximate root of the equation using Newton-Raphson method. Perform only 3 iterations with
.
Let G be an infinite group such that for any non-trivial subgroup H of . Then prove that
i) or H is infinite;
ii) If , then o(g) is infinite.
Which of the following statements are true, and which are false? Give reasons for your answers.
i) If k is a field, then so is .
ii) If R is an integral domain and I is an ideal of R, then .
iii) In a domain, every prime ideal is a maximal ideal.
iv) If R is a ring with zero divisors, and S is a subring of R, then S has zero divisors.
v) If R is a ring and is of degree
, then f(x) has exactly n roots in R.
For the following data, use Gauss backward difference method to obtain the interpolating polynomial f(x):
| x | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 |
| f(x) | 1.40 | 1.56 | 1.76 | 2.00 | 2.28 |
If , find the values of C1 and C2.
सरलतम रूप में एक ऐसा अंतर्वेशन बहुपद प्राप्त कीजिए जो निम्नलिखित आंकड़ों को आसंजित करता हो :
| x | -1 | 0 | 1 | 2 |
| f (x) | 3 | -4 | 5 | -6 |
Using Cayley’s theorem, find the permutation group to which a cyclic group of order 12 is isomorphic.