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Equality of Matrices

Let ax3 + b...

Question

Let $a x^{3} + b x^{2} + c x + d = ∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 2 x & 3 x 2 x + 3 & x + 1 & x 2 - x & 3 x + 4 & 5 x - 1 \end{matrix} ∣ ∣ ∣ ∣$ , then what is the value of $c ?$

A

- 1

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B

34

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C

35

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D

50

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Solution

The correct option is C $35$

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Similar questions

(3 x - 2)^{3} = a x^{3} + b x^{2} + c x + d

a + b + c + d =

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

then the value of

C

x^{2} + x + 1

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

, then real root of

a x^{3} + b x^{2} + c x + d = 0

∣ ∣ ∣ ∣ \begin{matrix} x - 1 & 5 x & 7 x^{2} - 1 & x - 1 & 8 2 x & 3 x & 0 \end{matrix} ∣ ∣ ∣ ∣

= a x^{3} + b x^{2} + c x + d

, then the value of c is given by

∣ ∣ ∣ ∣ \begin{matrix} x - 1 & 5 x & 7 x^{2} - 1 & x - 1 & 8 2 x & 3 x & 0 \end{matrix} ∣ ∣ ∣ ∣ = a x^{3} + b x^{2} + c x + d

c

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