(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).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(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.
Transcribed Image Text: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.
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