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I recently learnt a way to tackle these types of problems - Here I Learnt it, explained to me by @Pranjal Jain


f(x)=x4+ax3+bx2+cx+d f(x) = x^4 + ax^3 + bx^2 + cx + d

We can observe that -

f(e)=e×1993 f(e) = e\times1993

thus - f(11)11×1993=0f(11) - 11\times1993 = 0 , f(7)+7×1993=0f(-7) + 7\times1993 = 0

f(11)+f(7)=1993(117)=1993×4 f(11) + f(-7) = 1993(11 - 7) = 1993\times4

f(11)+f(7)4=1993\dfrac{f(11) + f(-7)}{4} = 1993

Where I am wrong , please don't provide me the answer , just comment where I am wrong.

Did I started wrongly i.e - f(e)=e×1993 f(e) = e\times1993 ?

Thank you

Note by U Z
4 years, 7 months ago

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1 vote

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Comments

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f(x)1993x,xRf(x) \neq 1993x, x \in \mathbb R

Krishna Sharma - 4 years, 7 months ago

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What is your reason behind the claim f(e)=1993e

Agnishom Chattopadhyay Staff - 4 years, 7 months ago

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Sorry I misunderstood it

U Z - 4 years, 7 months ago

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Wanna know the Wolfram|Alpha approach for this?

Agnishom Chattopadhyay Staff - 4 years, 7 months ago

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@Agnishom Chattopadhyay nope

U Z - 4 years, 7 months ago

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@U Z Hmm, I wish more people had read A=B and were exposed to EM

Agnishom Chattopadhyay Staff - 4 years, 7 months ago

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@Agnishom Chattopadhyay Should I delete this note because in a way I am discussing a problem

U Z - 4 years, 7 months ago

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@U Z Just delete that solution comment

Krishna Sharma - 4 years, 7 months ago

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Thank you! because of your note I also got a chance to learn .

shivamani patil - 4 years, 7 months ago

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Hey! You misunderstood it!! See. f(x)1993xf(x)-1993x has roots 1,21, 2 and 33. So we can say that f(x)1993x=(x1)(x2)(x3)(xα)f(x)-1993x=(x-1)(x-2)(x-3)(x-\alpha) (Since its of degree 4).

f(e)=ef(e)=e is for e=1,2,3e=1,2,3 only.

Carry on from here. I hope you got it this time.

Pranjal Jain - 4 years, 7 months ago

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@Calvin Lin As you see in the note, tag didn't worked! I didn't got any mail. Is there any bug? It happens a lot with me

Pranjal Jain - 4 years, 7 months ago

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@ mention currently only works in comments. It currently does not work in notes or problems

Calvin Lin Staff - 4 years, 7 months ago

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@Calvin Lin Sometimes it also causes trouble in comments. Lemme try here. @Pranjal Jain

Pranjal Jain - 4 years, 7 months ago

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I solved it see a comment is deleted after krishna's comment there i wrote the solution , thanks for helping

U Z - 4 years, 7 months ago

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