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C2 Help

Given that -1 is a root of the equation,

2 x^3 - 5 x^3 - 4 x + 3


find the two positive roots.



This shows up in the very first chapter of C2 which is about algebraic division, the remainder theorem etc.
Reply 1
Avatar for 2^1/2
2^1/2
11
if -1 is a root then (x+1) is a factor, and you say the chapter is about algebraic division...
Reply 2
Avatar for chowderspin
chowderspin
OP
Original post by 2^1/2
if -1 is a root then (x+1) is a factor, and you say the chapter is about algebraic division...



Id already found out that (x+1) is a factor, but i still don't get how that can be used to figure out the other two roots for the equation...
Reply 3
Avatar for StephenP91
StephenP91
3
Original post by chowderspin
Id already found out that (x+1) is a factor, but i still don't get how that can be used to figure out the other two roots for the equation...


Divide the cubic by the linear polynomial.

You have done long division with polynomials before have you not? I am assuming you have otherwise you can't do the question.

You simply divide. (2x3−5x3−4x+3)(2x^{3} - 5x^{3} - 4x + 3) by (x+1)(x + 1). From that, you'll get a quadratic and then if you factorise that, you'll get the other 2 roots for that cubic.
(edited 13 years ago)
Reply 4
Avatar for Thrug
Thrug
3
You could also equate the coefficients:

(x+1)(2x2+bx+3) (x + 1) ( 2x^2 +bx + 3)

...

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