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Inverse of a Function

Find the valu...

Question

Find the value of $a$ in the equation $(x + 1) (x + 2) (x + 3) = x^{3} + 6 x^{2} + (a x + b)$

A

11

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B

5

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C

4

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D

1

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Solution

The correct option is A $11$
The given equation is,
$(x + 1) (x + 2) (x + 3) = x^{3} + 6 x^{2} + a x + b$ (1)

Now, $(x + 1) (x + 2) = x^{2} + 3 x + 2$
Putting this value in equation (1), we get,
$(x^{2} + 3 x + 2) (x + 3) = x^{3} + 6 x^{2} + a x + b$

$∴ x^{3} + 3 x^{2} + 3 x^{2} + 9 x + 2 x + 6 = x^{3} + 6 x^{2} + a x + b$

$∴ x^{3} + 6 x^{2} + 11 x + 6 = x^{3} + 6 x^{2} + a x + b$

Comparing coefficients of $x^{3}$ , $x^{2}$ , $x$ and constat terms on LHS and RHS, we get,
$a = 11$ and $b = 6$
Thus, Answer is option (A)

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