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21 Jul 2007, 16:45
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I am having a rough time understanding this equation (see below) - in which I mean that I am not clear as to the definition of a positive root. Does this follow the rule from Decarte's therom? I am lost as to how if you have all positive co-efficients - what is the rule that explains why the product cannot produce any positive roots.
1.If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots.
Eg: x3+3x2+2x+6=0 has no positive roots
1.If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots.
Eg: x3+3x2+2x+6=0 has no positive roots
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21 Jul 2007, 17:20
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noah
i don't know Descarte's theorem but factor by grouping
x^2(x+3) +2(x+3)
(x^2+2)(x+3)
x=-3
x^2+2=0 has no real solution because
x^2=-2 is imaginary
as far as the positive roots
and equation in the form : x^2+2ax+a^2
can is factored to (x+a)^2
the solution to the equation is x=-a
21 Jul 2007, 23:52
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Think about it... you need something to be negative to make the equation zero. If the co-efficients are all positive, the variable will have to be a negative to yield a ZERO.
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Hi there,
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Thank you for understanding, and happy exploring!
