Raízes em P.A.

por Betoneira de Natal Qui 14 Abr 2022, 00:53

Mostre que a equação

Raízes em P.A. Svg+xml;base64,<?xml version='1.0' encoding='UTF-8'?>
<!-- Generated by CodeCogs with dvisvgm 2.11.1 -->
<svg version='1.1' xmlns='http://www.w3.org/2000/svg' xmlns:xlink='http://www.w3.org/1999/xlink' width='100.419738pt' height='12.697312pt' viewBox='-.239051 -.234916 100.419738 12.697312'>
<defs>
<path id='g2-43' d='M4.770112-2.761644H8.069738C8.237111-2.761644 8.452304-2.761644 8.452304-2.976837C8.452304-3.203985 8.249066-3.203985 8.069738-3.203985H4.770112V-6.503611C4.770112-6.670984 4.770112-6.886177 4.554919-6.886177C4.327771-6.886177 4.327771-6.682939 4.327771-6.503611V-3.203985H1.028144C.860772-3.203985 .645579-3.203985 .645579-2.988792C.645579-2.761644 .848817-2.761644 1.028144-2.761644H4.327771V.537983C4.327771 .705355 4.327771 .920548 4.542964 .920548C4.770112 .920548 4.770112 .71731 4.770112 .537983V-2.761644Z'/>
<path id='g2-48' d='M5.355915-3.825654C5.355915-4.817933 5.296139-5.786301 4.865753-6.694894C4.375592-7.687173 3.514819-7.950187 2.929016-7.950187C2.235616-7.950187 1.3868-7.603487 .944458-6.611208C.609714-5.858032 .490162-5.116812 .490162-3.825654C.490162-2.666002 .573848-1.793275 1.004234-.944458C1.470486-.035866 2.295392 .251059 2.917061 .251059C3.957161 .251059 4.554919-.37061 4.901619-1.06401C5.332005-1.960648 5.355915-3.132254 5.355915-3.825654ZM2.917061 .011955C2.534496 .011955 1.75741-.203238 1.530262-1.506351C1.398755-2.223661 1.398755-3.132254 1.398755-3.969116C1.398755-4.94944 1.398755-5.834122 1.590037-6.539477C1.793275-7.340473 2.402989-7.711083 2.917061-7.711083C3.371357-7.711083 4.064757-7.436115 4.291905-6.40797C4.447323-5.726526 4.447323-4.782067 4.447323-3.969116C4.447323-3.16812 4.447323-2.259527 4.315816-1.530262C4.088667-.215193 3.335492 .011955 2.917061 .011955Z'/>
<path id='g2-61' d='M8.069738-3.873474C8.237111-3.873474 8.452304-3.873474 8.452304-4.088667C8.452304-4.315816 8.249066-4.315816 8.069738-4.315816H1.028144C.860772-4.315816 .645579-4.315816 .645579-4.100623C.645579-3.873474 .848817-3.873474 1.028144-3.873474H8.069738ZM8.069738-1.649813C8.237111-1.649813 8.452304-1.649813 8.452304-1.865006C8.452304-2.092154 8.249066-2.092154 8.069738-2.092154H1.028144C.860772-2.092154 .645579-2.092154 .645579-1.876961C.645579-1.649813 .848817-1.649813 1.028144-1.649813H8.069738Z'/>
<path id='g1-50' d='M2.247572-1.625903C2.375093-1.745455 2.709838-2.008468 2.83736-2.12005C3.331507-2.574346 3.801743-3.012702 3.801743-3.737983C3.801743-4.686426 3.004732-5.300125 2.008468-5.300125C1.052055-5.300125 .422416-4.574844 .422416-3.865504C.422416-3.474969 .73325-3.419178 .844832-3.419178C1.012204-3.419178 1.259278-3.53873 1.259278-3.841594C1.259278-4.25604 .860772-4.25604 .765131-4.25604C.996264-4.837858 1.530262-5.037111 1.920797-5.037111C2.662017-5.037111 3.044583-4.407472 3.044583-3.737983C3.044583-2.909091 2.462765-2.303362 1.522291-1.338979L.518057-.302864C.422416-.215193 .422416-.199253 .422416 0H3.57061L3.801743-1.42665H3.55467C3.53076-1.267248 3.466999-.868742 3.371357-.71731C3.323537-.653549 2.717808-.653549 2.590286-.653549H1.171606L2.247572-1.625903Z'/>
<path id='g1-52' d='M3.140224-5.156663C3.140224-5.316065 3.140224-5.379826 2.972852-5.379826C2.86924-5.379826 2.86127-5.371856 2.781569-5.260274L.239103-1.570112V-1.307098H2.486675V-.645579C2.486675-.350685 2.462765-.263014 1.849066-.263014H1.665753V0C2.343213-.02391 2.359153-.02391 2.81345-.02391S3.283686-.02391 3.961146 0V-.263014H3.777833C3.164134-.263014 3.140224-.350685 3.140224-.645579V-1.307098H3.985056V-1.570112H3.140224V-5.156663ZM2.542466-4.511083V-1.570112H.518057L2.542466-4.511083Z'/>
<path id='g0-97' d='M3.598506-1.422665C3.53873-1.219427 3.53873-1.195517 3.371357-.968369C3.108344-.633624 2.582316-.119552 2.020423-.119552C1.530262-.119552 1.255293-.561893 1.255293-1.267248C1.255293-1.924782 1.625903-3.263761 1.853051-3.765878C2.259527-4.60274 2.82142-5.033126 3.287671-5.033126C4.076712-5.033126 4.23213-4.052802 4.23213-3.957161C4.23213-3.945205 4.196264-3.789788 4.184309-3.765878L3.598506-1.422665ZM4.363636-4.483188C4.23213-4.794022 3.90934-5.272229 3.287671-5.272229C1.936737-5.272229 .478207-3.526775 .478207-1.75741C.478207-.573848 1.171606 .119552 1.984558 .119552C2.642092 .119552 3.203985-.394521 3.53873-.789041C3.658281-.083686 4.220174 .119552 4.578829 .119552S5.224408-.095641 5.439601-.526027C5.630884-.932503 5.798257-1.661768 5.798257-1.709589C5.798257-1.769365 5.750436-1.817186 5.678705-1.817186C5.571108-1.817186 5.559153-1.75741 5.511333-1.578082C5.332005-.872727 5.104857-.119552 4.614695-.119552C4.267995-.119552 4.244085-.430386 4.244085-.669489C4.244085-.944458 4.27995-1.075965 4.387547-1.542217C4.471233-1.841096 4.531009-2.10411 4.62665-2.450809C5.068991-4.244085 5.176588-4.674471 5.176588-4.746202C5.176588-4.913574 5.045081-5.045081 4.865753-5.045081C4.483188-5.045081 4.387547-4.62665 4.363636-4.483188Z'/>
<path id='g0-98' d='M2.761644-7.998007C2.773599-8.045828 2.797509-8.117559 2.797509-8.177335C2.797509-8.296887 2.677958-8.296887 2.654047-8.296887C2.642092-8.296887 2.211706-8.261021 1.996513-8.237111C1.793275-8.225156 1.613948-8.201245 1.398755-8.18929C1.111831-8.16538 1.028144-8.153425 1.028144-7.938232C1.028144-7.81868 1.147696-7.81868 1.267248-7.81868C1.876961-7.81868 1.876961-7.711083 1.876961-7.591532C1.876961-7.507846 1.78132-7.161146 1.733499-6.945953L1.446575-5.798257C1.327024-5.32005 .645579-2.606227 .597758-2.391034C.537983-2.092154 .537983-1.888917 .537983-1.733499C.537983-.514072 1.219427 .119552 1.996513 .119552C3.383313 .119552 4.817933-1.661768 4.817933-3.395268C4.817933-4.495143 4.196264-5.272229 3.299626-5.272229C2.677958-5.272229 2.116065-4.758157 1.888917-4.519054L2.761644-7.998007ZM2.008468-.119552C1.625903-.119552 1.207472-.406476 1.207472-1.338979C1.207472-1.733499 1.243337-1.960648 1.458531-2.797509C1.494396-2.952927 1.685679-3.718057 1.733499-3.873474C1.75741-3.969116 2.462765-5.033126 3.275716-5.033126C3.801743-5.033126 4.040847-4.507098 4.040847-3.88543C4.040847-3.311582 3.706102-1.960648 3.407223-1.338979C3.108344-.6934 2.558406-.119552 2.008468-.119552Z'/>
<path id='g0-99' d='M4.674471-4.495143C4.447323-4.495143 4.339726-4.495143 4.172354-4.351681C4.100623-4.291905 3.969116-4.112578 3.969116-3.921295C3.969116-3.682192 4.148443-3.53873 4.375592-3.53873C4.662516-3.53873 4.985305-3.777833 4.985305-4.25604C4.985305-4.829888 4.435367-5.272229 3.610461-5.272229C2.044334-5.272229 .478207-3.56264 .478207-1.865006C.478207-.824907 1.123786 .119552 2.343213 .119552C3.969116 .119552 4.99726-1.147696 4.99726-1.303113C4.99726-1.374844 4.925529-1.43462 4.877709-1.43462C4.841843-1.43462 4.829888-1.422665 4.722291-1.315068C3.957161-.298879 2.82142-.119552 2.367123-.119552C1.542217-.119552 1.279203-.836862 1.279203-1.43462C1.279203-1.853051 1.482441-3.012702 1.912827-3.825654C2.223661-4.387547 2.86924-5.033126 3.622416-5.033126C3.777833-5.033126 4.435367-5.009215 4.674471-4.495143Z'/>
<path id='g0-120' d='M5.66675-4.877709C5.284184-4.805978 5.140722-4.519054 5.140722-4.291905C5.140722-4.004981 5.36787-3.90934 5.535243-3.90934C5.893898-3.90934 6.144956-4.220174 6.144956-4.542964C6.144956-5.045081 5.571108-5.272229 5.068991-5.272229C4.339726-5.272229 3.93325-4.554919 3.825654-4.327771C3.550685-5.224408 2.809465-5.272229 2.594271-5.272229C1.374844-5.272229 .729265-3.706102 .729265-3.443088C.729265-3.395268 .777086-3.335492 .860772-3.335492C.956413-3.335492 .980324-3.407223 1.004234-3.455044C1.41071-4.782067 2.211706-5.033126 2.558406-5.033126C3.096389-5.033126 3.203985-4.531009 3.203985-4.244085C3.203985-3.981071 3.132254-3.706102 2.988792-3.132254L2.582316-1.494396C2.402989-.777086 2.056289-.119552 1.422665-.119552C1.362889-.119552 1.06401-.119552 .812951-.274969C1.243337-.358655 1.338979-.71731 1.338979-.860772C1.338979-1.099875 1.159651-1.243337 .932503-1.243337C.645579-1.243337 .334745-.992279 .334745-.609714C.334745-.107597 .896638 .119552 1.41071 .119552C1.984558 .119552 2.391034-.334745 2.642092-.824907C2.833375-.119552 3.431133 .119552 3.873474 .119552C5.092902 .119552 5.738481-1.446575 5.738481-1.709589C5.738481-1.769365 5.69066-1.817186 5.618929-1.817186C5.511333-1.817186 5.499377-1.75741 5.463512-1.661768C5.140722-.609714 4.447323-.119552 3.90934-.119552C3.490909-.119552 3.263761-.430386 3.263761-.920548C3.263761-1.183562 3.311582-1.374844 3.502864-2.163885L3.921295-3.789788C4.100623-4.507098 4.507098-5.033126 5.057036-5.033126C5.080946-5.033126 5.415691-5.033126 5.66675-4.877709Z'/>
</defs>
<g id='page1' transform='matrix(1.13 0 0 1.13 -63.986043 -62.879193)'>
<use x='56.413267' y='65.753425' xlink:href='#g0-97'/>
<use x='62.558211' y='65.753425' xlink:href='#g0-120'/>
<use x='69.210299' y='60.817239' xlink:href='#g1-52'/>
<use x='76.599277' y='65.753425' xlink:href='#g2-43'/>
<use x='88.360592' y='65.753425' xlink:href='#g0-98'/>
<use x='93.337697' y='65.753425' xlink:href='#g0-120'/>
<use x='99.989784' y='60.817239' xlink:href='#g1-50'/>
<use x='107.378763' y='65.753425' xlink:href='#g2-43'/>
<use x='119.140078' y='65.753425' xlink:href='#g0-99'/>
<use x='127.498896' y='65.753425' xlink:href='#g2-61'/>
<use x='139.924376' y='65.753425' xlink:href='#g2-48'/>
</g>
</svg>

, com (a ≠ 0) possui raízes reais em progressão aritmética se e só se 9b² = 100ac

Sendo biquadrada, eu pensei em:

->

Como ele pede raízes reais, e sabendo que (9b² = 100ac -> 3b = 10√ac ), logo:

Ou seja, pelas contas, está certo afirmar que 3b = 10√ac

Porém, como consigo relacionar isso as raízes?
Eu tentei abrir em casos onde isso poderia acontecer, e só consegui relacionar raízes do tipo( -3k , -k , +k , +3k ) mas não sei se essa análise está certa...

por **Elcioschin** Qui 14 Abr 2022, 17:41

a.x⁴ + 0.x³ + b.x² + 0.x + c

Raízes em PA ---> (k - 3.r) , (k - r) , (k + r) , (k + 3.r) ---> 2.r = razão e k uma constante

Relações de Girard

(k - 3.r) + (k - r) + (k + r) + (k + 3.r) = -0/a ---> k = 0 --> PA = - 3.r , - r , r , 3.r

(- 3.r).(- r) + (- 3.r).r + (- 3.r).(3.r) + (- r).r ,+ (- r).(3.r) + r.(3.r) = b/a ---> - 10.r² = b/a

Tente completar