### Gönderen Konu: polinom  (Okunma sayısı 3359 defa)

#### stuart clark

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##### polinom
« : Haziran 18, 2011, 05:56:57 ös »
if  $f(x) = x^3+ax^2+bx+c$ has 3  distinct real

roots and $\left(x^2 +2x+2\right)^3+ a\left(x^2+2x+2\right)^2 +b\left(x^2+2x+2\right)+c$

has no real roots. then find  $a,b,c$

#### scarface

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##### Ynt: polinom
« Yanıtla #1 : Haziran 19, 2011, 03:04:15 ös »
Let's assume that roots of f(x) = 0 are x1, x2, x3. So we have to solve that x2 + 2x + 2 = xi. (i = 1, 2, 3). Since equation x2 + 2x + 2 - xi = 0 has not real roots, then its discriminant must be negative. That is Δ = 22 - 4(2 - xi ) < 0. Therefore xi < 1.

for example

if f(x) = x(x + 1)(x + 2), then a = 3, b = 2, c = 0.

if f(x) = x(x + 1)(x + 3), then a = 4, b = 3, c = 0.

We can see that a, b, c aren't constant. we don't find unique value of a,b,c.
Uğraşınca çözebileceğim zorlukta olan soruları çözmeyi severim.