(6) Let PW) be a polynomiel with complex coefticieabs, and Let 1eC be a root of Pla). Then the conjugate a is also a root of PlW. True. The roobs of Pu) always come in conjugate peirs. True. This is also why the conjugate of an eigenvalue (nan)-metrix A over & is itself an eigenvelue of A. O False. A counteiexample is Ehe yolynominl Pa)=x-1, which has only one rook, namely 1. In porticular, T camnot be a in root of PlW).
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
(11) which option a,b,c or d is correct based on the question in the picture. THERE IS ONLY 1 correct option.
![9.
Let Pla) be a polyn om iel with complex coefticien bs, and let 1e C
be a root of Pl). Then the conjugate a is also a root of PlW.
True, The roobs of Plk) always come in conjugete peirs.
) True. This is also why the conjugate of an eigenvalue of in
(nan)-metrie A over &
C is itself an eigenvalue of A.
False. A counterexample is the yolynomial Pulex-d, which
has only one root, nAmely 1. In porticular, ī camnot be a
root of Pu).
O False. This does not hold in general, but it does apply if all
coefticien bs of Pla) are real.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fcafa15-2b3d-496b-99e7-5b98e8b2de11%2F311ed31a-9fa1-435c-88d1-071d443359b4%2Fiyrrk34_processed.png&w=3840&q=75)
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