Hi, I' not sure if I've done this question correctly so I just want someone to tell me where I've gone wrong (if I have).(adsbygoogle = window.adsbygoogle || []).push({});

Evaluate the following determinant as a product of two terms. Hence find, in terms of p the values of x for which it vanishes.

Grr, I can't seem to use LaTeX properly so I'll just "draw" the determinant:

x x 0

0 x p

-2x -p x

[tex]= x \left\vert \begin{array}{cc} x & p\\-p & x \end{array}\right\vert - x \left\vert \begin{array}{cc} 0 & p\\-2x & x \end{array}\right\vert[/tex]

= x(x^2 + p^2) - x(2xp)

=x^3 + p^2.x - 2x^2.p

- x(x^2 - 2px + p^2) = 0

x = {-(-2p) +- [(-2p)^2 - 4.1.p^2]^1/2}/2

x = [2p +- (4p^2 - 4p^2)^1/2]/2

x = p

It doesn't look right to me :/.

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# Homework Help: Determinants question

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