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

#Algebra

Easy Math Editor

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Comments

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 $x = 1$

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

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

Siddhartha Srivastava - 6 years, 7 months ago

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

Eshan Abbas - 6 years, 7 months ago

Thanks. Corrected. Hopefully correct now.

Siddhartha Srivastava - 6 years, 7 months ago

thats what he got bro

Saurav Zuer - 6 years, 7 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}`	$\boxed{123}$