## 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 4 million people

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

including olympiad champions, researchers, and professionals.

## 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 – Anik Mandal · 1 year, 8 months ago

Log in to reply

Use the Table of Differences method to solve first one. – Anik Mandal · 1 year, 8 months ago

Log in to reply

The first one can be done by Lagrange's Interpolation method. – Akshat Sharda · 1 year, 8 months ago

Log in to reply

– Arko Roychoudhury · 1 year, 8 months ago

thanksLog in to reply