Polynomial

Given \(P\) is a polynomial that is not constant, satisfy \( P\left( P(x) \right) = (x^2 + x +1) \times P(x) \) for every real \(x\). Find \( P(10) \).

Note by Fidel Simanjuntak
12 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Hint: Let \(d\) denote the degree of polynomial \(P(x) \), then the degree of LHS is \(2d\), and the degree of RHS is \(d+2\). So can you solve for \(d\)? And can you determine the function \(P(x) \)?

Pi Han Goh - 12 months ago

Log in to reply

I got \( P(x) = x^2 + x\) but I dont know, maybe there's another possible formula for \( P(x) \)

Fidel Simanjuntak - 12 months ago

Log in to reply

No, there isn't. If you try for (constant of quadratic polynomial not equal 0), then you get a system of equations that has no solution.

I know that this isn't the best/fastest way to get the answer, but it works!

Pi Han Goh - 12 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...