Will anyone help me with this?

A function is given $f(x)= 2x^{4} - 3x^{3} + 4x^{2} - 5x +6$ , calculate the sum of $S= A+B+C+D+E$ , if $f(x)= A(x-1)^{4} + B(x-1)^{3} + C(x-1)^{2} + D(x-1) +E$

#Function

Easy Math Editor

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`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`	$\sum_{i=1}^3$
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`\boxed{123}`	$\boxed{123}$

Comments

Make the substitution x = z - 1 and expand f(x) to get 2z^5 + 5z^4 + 7z^2 + 2z + 4. Hence, S = 2 + 5 + 7 + 2 + 4 = 20.

Michael Mendrin - 7 years, 3 months ago

Wouldn't we take $x = z + 1$ . Because If $x = z - 1$ , we'd have $x + 1 = z$ and the f(x) you got would be $2(x+1)^5 \ldots$ .

Siddhartha Srivastava - 7 years, 3 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}`	$\boxed{123}$