Waste less time on Facebook — follow Brilliant.
×

JEE MAIN

If f(x) = x^4 + ax^3 + bx^2 + cx + d, and f(2)= 1, f(3) = 2, f(4) = 3, f(5) = 4, what is the value of a + b + c + d ? Please find it out as soon as possible. I am having problems in finding it out

Note by Eshan Abbas
3 years 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

Let \( g(x) = f(x) - x + 1 \).Then \(g(x) \) is of degree \( 4\). And for \( x =2,3,4,5 \), \( g(x) = 0 \).This implies \( 2,3,4,5 \) are the roots of \( g(x) \).

Thus we can write \( g(x) = (x-2)(x-3)(x-4)(x-5) \)

\( \Rightarrow f(x) - x + 1 = (x-2)(x-3)(x-4)(x-5) \)

\( \Rightarrow x^4 + ax^3 + bx^2 + cx + d - x + 1 = (x-2)(x-3)(x-4)(x-5) \).

Putting \( x = 1 \)

\( \Rightarrow 1^4 + a*1^3 + b*1^2 + c*1 + d - 1 + 1 = (1-2)(1-3)(1-4)(1-5) \)

\( \Rightarrow a+b+c+d = 24-1 = 23 \).

Log in to reply

I think that g(x) should be equal to f(x) - x + 1

Eshan Abbas - 3 years ago

Log in to reply

Thanks. Corrected. Hopefully correct now.

Log in to reply

thats what he got bro

Saurav Zuer - 2 years, 11 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...