Help!Please comment

This problem

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

$f(x) = x^4 + ax^3 + bx^2 + cx + d$

We can observe that -

$f(e) = e\times1993$

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

$f(11) + f(-7) = 1993(11 - 7) = 1993\times4$

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

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

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

Thank you

Easy Math Editor

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
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Comments

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

Krishna Sharma - 6 years, 5 months ago

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

Agnishom Chattopadhyay - 6 years, 5 months ago

Sorry I misunderstood it

U Z - 6 years, 5 months ago

Wanna know the Wolfram|Alpha approach for this?

Agnishom Chattopadhyay - 6 years, 5 months ago

@Agnishom Chattopadhyay – nope

U Z - 6 years, 5 months ago

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

Agnishom Chattopadhyay - 6 years, 5 months ago

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

U Z - 6 years, 5 months ago

@U Z – Just delete that solution comment

Krishna Sharma - 6 years, 5 months ago

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

shivamani patil - 6 years, 5 months ago

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

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

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

Pranjal Jain - 6 years, 5 months ago

@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 - 6 years, 5 months ago

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

Calvin Lin Staff - 6 years, 5 months ago

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

Pranjal Jain - 6 years, 5 months ago

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

U Z - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$