Free Essay

I Like Cake

In: Computers and Technology

Submitted By janx1787
Words 397
Pages 2
Matematik aflevering til d. 05/09/12
Opgave 1
Jeg er blevet givet ligningen: 7x ² - 3x + 5 = 0

Jeg vil løse ligningen grafisk vha. Geo-Gebra:
Da parablen ikke rammer x-aksen, er der derfor ingen løsning til ligningen. Sagt på en anden måde, diskriminaten er minus.

Jeg vil løse ligningen: -x ² - 5x - 6 = 0
Jeg vil denne gang bruge samme fremgangsmåde.

Denne parabel rammer x-aksen 2 steder, diskriminanten for denne parabel er derfor positiv.

Vores 2 løsninger til denne ligning er derfor således:
-3 eller -2

Jeg vil løse ligningen: 2(x - 1)(x + 4) = 0
Jeg vil igen bruge Geo-gebra til at beregne den.

Vores parabel rammer igen 2 steder på x-aksen, vi har derfor 2 løsninger, 2 rødder. Diskriminanten er positiv.

Vores løsninger er:
-4 eller 1

Jeg vil beregne de 3 førnævnte ligninger analytisk.

Jeg vil starte med ligningen: 7x ² - 3x + 5 = 0

Jeg starter med at regne diskriminanten: d=b2-4ac⟺d=-32-4∙7∙5⟺d=-131 Som vi også fandt ud af tidligere, så har denne ligning ingen løsning, da diskriminanten er negativ.

Jeg vil nu løse ligningen: -x ² - 5x - 6 = 0

Diskriminanten: d=b2-4ac⟺d=-52-4∙-1∙-6⟺d=1 Diskriminanten er 1, vi har derfor 2 løsninger.
Dem vil jeg finde vha. diskriminantformelen:



Vi har nu fundet de 2 løsninger til ligningen: x=-3 eller-2

Jeg vil nu løse ligningen: 2(x - 1)(x + 4)=0

Jeg vil allerførst reducere ligningen:

Vi har nu reduceret vores ligning til: 2x2+6x-8=0

Diskriminanten: d=b2-4ac⟺d=62-4∙2∙-8⟺d=100 Diskriminanten er positiv, og der er derfor 2 rødder, 2 resultater.



Vi har derfor 2 løsninger: x=1 eller-4
Opgave 2
Tre forskellige andengradspolynomier er givet: f1,f2,f3
De er alle 3 på formen: fx=ax2+bx+c

A f1:a=+ og c=- f2:a=+ og c=+ f3:a= - og c= +

B f1:2 rødder f2:0 rødder f3:2 rødder

C f1: d=+ f2:d=0 f3:d=+

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