Let begin vmatrix x - 2 - xx- 2 - x - 6 1x - x - 6end vmatrix -A x- 4-B x- 3-C x- 2-D x-E

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Standard XII

Mathematics

Determinant

Let begin vma...

Question

Let $∣ ∣ ∣ ∣ \begin{matrix} x & 2 & x x^{2} & x & 6 x & x & 6 \end{matrix} ∣ ∣ ∣ ∣ = A x^{4} + B x^{3} + C x^{2} + D x + E$

A+B+C+D = 0

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A+B+C+D = -1

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5A+4B+3C+2D+E = -11

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5A+4B+3C+2D+E = 11

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Solution

The correct options are
A A+B+C+D = 0
C 5A+4B+3C+2D+E = -11
Expand det. And equate
A = 1, B = -1, C = -12, D = 12, E = 0

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Similar questions

Q. .Let

∣ ∣ ∣ ∣ \begin{matrix} x & 2 & x x^{2} & x & 6 x & x & 6 \end{matrix} ∣ ∣ ∣ ∣

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

,then the value of 5a + 4b + 3c + 2d + e is
equal to

Q. Let

∣ ∣ ∣ ∣ \begin{matrix} x & 2 & x x^{2} & x & 6 x & x & 6 \end{matrix} ∣ ∣ ∣ ∣ = A x^{4} + B x^{3} + C x^{2} + D x + E

, then the value of 5A + 4B + 3C + 2D + E is equal to

Q. 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 =

Let
$\begin{matrix} ∣ ∣ ∣ ∣ \begin{matrix} x & 2 & x x^{2} & x & 6 x & x & 6 \end{matrix} ∣ ∣ ∣ ∣ & = A x^{4} + B x^{3} + C x^{2} + D x + E \end{matrix}$

Q. If

∣ ∣ ∣ ∣ \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

Then value of

ϱ

equals to,

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Let ∣∣ ∣∣x2xx2x6xx6∣∣ ∣∣=Ax4+Bx3+Cx2+Dx+E

The correct options are A A+B+C+D = 0 C 5A+4B+3C+2D+E = -11Expand det. And equate A = 1, B = -1, C = -12, D = 12, E = 0

Let $∣ ∣ ∣ ∣ \begin{matrix} x & 2 & x x^{2} & x & 6 x & x & 6 \end{matrix} ∣ ∣ ∣ ∣ = A x^{4} + B x^{3} + C x^{2} + D x + E$

The correct options are
A A+B+C+D = 0
C 5A+4B+3C+2D+E = -11
Expand det. And equate
A = 1, B = -1, C = -12, D = 12, E = 0