## Excel in math and science

### Master concepts by solving fun, challenging problems.

## It's hard to learn from lectures and videos

### Learn more effectively through short, conceptual quizzes.

## Our wiki is made for math and science

###
Master advanced concepts through explanations,

examples, and problems from the community.

## Used and loved by over 5 million people

###
Learn from a vibrant community of students and enthusiasts,

including olympiad champions, researchers, and professionals.

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

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

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestQ2. Let the fourth root be \(\alpha\)

Then the polynomial can be written as \(P(x) = (x-1)(x-2)(x-3)(x-\alpha)\)

Now \(P(0)= (0-1)(0-2)(0-3)(0-\alpha) = 6\alpha\)

AND \(P(4) = (4-1)(4-2)(4-3)(4-\alpha) = 24-6\alpha\)

Therefore \(P(0) + P(4) = 6\alpha+24-6\alpha = 24\) !Done

Log in to reply

Use the Table of Differences method to solve first one.

Log in to reply

The first one can be done by Lagrange's Interpolation method.

Log in to reply

thanks

Log in to reply