how can i find the roots of this characteristic equation: r^2 -6r - 2 = 0 ?

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how can i find the roots of this characteristic equation: r^2 -6r - 2 = 0 ?

guys i'm working on the second order differential equation. just for your information

2007-07-28 12:47:04 · 3 answers · asked by aren b 1 in Science & Mathematics ➔ Mathematics

3 answers

complete the square

(r - 3)^2 - 9 -2 = 0
(r-3)^2 = 11
(r-3) = +-sqrt(11)
r = 2 +-sqrt(11)

2007-07-28 12:52:11 · answer #1 · answered by Martin C 1 · 0⤊ 0⤋

r^2 - 6r -2 = 0
r = [ 6 +or- sqrt( 36 - 4(1)(-2) ) ] / 2
= [ 6 +or- sqrt(44) ] / 2
= [ 6 +or- 6.633 ] /2
= 12.633/2 or -0.633/2
= 6.317 or -0.317
this is the quadratic formula

2007-07-28 20:08:32 · answer #2 · answered by vlee1225 6 · 0⤊ 0⤋

Why not treat it as a quadratic and do the roots?

2007-07-28 19:55:12 · answer #3 · answered by Swamy 7 · 0⤊ 1⤋