If - - x - 1 5 x 7- x 2 - 1 x - 1 8- 2 x 3 x 0 - - a x 3 - b x 2 - c x - d then value of c is given by

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Properties of Determinants

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Question

If $∣ ∣ ∣ ∣ \begin{matrix} x - 1 & 5 x & 7 x^{2} - 1 & x - 1 & 8 2 x & 3 x & 0 \end{matrix} ∣ ∣ ∣ ∣ = a x^{3} + b x^{2} + c x + d$ then value of $c$ is given by

1

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Solution

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Similar questions

∣ ∣ ∣ ∣ \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

∣ ∣ ∣ ∣ ∣ \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

C

x^{2} + x + 1

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

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

- a + b - c + d

(x - \frac{1}{5}) (x + 1) (x + \frac{3}{7})

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

x

∣ ∣ ∣ ∣ \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

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