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Inequalities Involving Mathematical Means

One root of t...

Question

One root of the equation (x+1)(x+3)(x+2)(x+4)=120 is

A

-1

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B

2

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C

1

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D

0

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Solution

The correct option is D 1
$120 = 5! = 5.4.3.2.1$
$= 2 \times 3 \times 4 \times 5$
$= (x + 4) (x + 3) (x + 2) (x + 1)$
By observation, using $x = 1$ , we will get the product as $120$
Hence, $x = 1$ is one root.

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