The number of rational root of $(x + 1) (x + 2) (x + 3) (x + 4) = 24$ is:

3

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2

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1

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0

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Solution

The correct option is B $2$
$(x + 1) (x + 2) (x + 3) (x + 4) = 24$
$\Rightarrow x^{4} + 10 x^{3} + 35 x^{2} + 50 x =$ $x . (x^{3} + 10 x^{2} + 35 x + 50)$
By hit and trail method we have $x = - 5$ as root of $(x^{3} + 10 x^{2} + 35 x + 50)$ dividing it with the equation we get quotient
$x . (x + 5) (x^{2} + 5 x + 10)$
$(x^{2} + 5 x + 10)$ has complex irrational roots
Hence the rational roots are $x = - 5, 0$

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