If a- b- c are distinct- then the value of x satisfying 0 - 2-a x 3-b x 2-a 0 x 2-c x 4-b x-c 0-0 isa cb ac bd 0

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Proof by mathematical induction

If a, b, c ar...

Question

If a, b, c are distinct, then the value of x satisfying $|\begin{matrix} 0 & x^{2} - a & x^{3} - b \\ x^{2} + a & 0 & x^{2} + c \\ x^{4} + b & x - c & 0 \end{matrix}| = 0 is$
(a) c
(b) a
(c) b
(d) 0

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If $a, b, c$ are different real numbers and $x$ is a variable then a factor of the determinant

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 0 & x^{2} - a & x^{3} - b x^{2} + a & 0 & x^{2} + c x^{4} + b & x - c & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣$ is

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 0 & x^{2} - a & x^{3} - b x^{2} + a & 0 & x^{2} + c x^{4} + b & x - c & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣

f (x) = 0

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a (x^{2} + 4 x + 4)^{2} + b (x^{2} + 4 x + 4) + c = 0

1, 2, 3

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

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