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Composite Function

If a x ∧ 4+b ...

Question

If $a x^{4} + b x^{3} + c x^{2} + d x + e = ∣ ∣ ∣ ∣ \begin{matrix} x^{3} + 3 x & x - 1 & x + 3 x + 1 & - 2 x & x - 4 x - 3 & x + 4 & 3 x \end{matrix} ∣ ∣ ∣ ∣$ , then e =

A

1

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B

0

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C

2

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D

-1

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Solution

The correct option is B
0

put x = 0, in the given equation on both sides

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Similar questions

a x^{4} + b x^{3} + c x^{2} + d x + e

∣ ∣ ∣ ∣ \begin{matrix} x^{3} + 3 x & x - 1 & x + 3 x + 1 & - 2 x & x - 4 x - 3 & x + 4 & 3 x \end{matrix} ∣ ∣ ∣ ∣

e = 0

a x^{4} + b x^{3} + c x^{2} + d x + e = ∣ ∣ ∣ ∣ \begin{matrix} x^{3} + 3 x & x - 1 & x + 3 x + 1 & - 2 x & x - 4 x - 3 & x + 4 & 3 x \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} x + 2 & 2 x + 3 & 3 x + 4 2 x + 3 & 3 x + 4 & 4 x + 5 3 x + 5 & 5 x + 8 & 10 x + 17 \end{matrix} ∣ ∣ ∣ ∣ = 0

x

\int (x^{3} - 2 x^{2} + 5) e^{3 x} d x = e^{3 x} (A x^{3} + B x^{2} + C x + D)

then the statement which is incorrect is

∣ ∣ ∣ ∣ \begin{matrix} x^{2} + 3 x & x + 1 & x - 2 x - 1 & 1 - 2 x & x + 4 x + 3 & x - 4 & 3 x \end{matrix} ∣ ∣ ∣ ∣ = A x^{4} + B x^{3} + C x^{2} + D x + ϱ

ϱ

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