3 replies to this topic

[The Conqueror]

I'm trying to solve this cubic equation. The roots are 2, 2 and 5 but the output is only 2 and 5. How can I determime which root is repeated?
X^3-9X^2+24X-20=0
I am using fx-991ES

Edited by The Conqueror, 17 May 2014 - 10:57 AM.

[pan.gejt]

use polynomial division for determining the 3rd root.

Edited by pan.gejt, 28 May 2014 - 10:25 AM.

[pan.gejt]

I found smarter and faster solution

Take the last term which is 20 and divide it by multiplication of obtained roots 2×5

So x = 20/(5×2) = 20/10 = 2

Do not forget to check the sign (plus or minus) of the last term: (x-2)×(x-2)×(x-5) gives (-2)×(-2)×(-5) = -20 which corresponds to the last term of equation.

[sammy134]

Ive had to solve many cubics in the past, and most of the time the repeated root was always the x2 that showed up so the second answer. My calculator spit out x1 = 5, and x2= 2. I always took x2 to be the repeated and double chekced by subbing it back in, and it worked