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Fantezi Cebir => Fantezi Cebir => Konuyu başlatan: stuart clark - Ekim 21, 2012, 05:32:47 öö

Başlık: Cubic polynomial
Gönderen: stuart clark - Ekim 21, 2012, 05:32:47 öö

Let a,b,c,d be four integers such that ad is odd and bc is even,then ax³+bx²+cx+d = 0 has

options::

(a) at least  one irrational roots
(b) all three rational roots
(c) all three integral roots
(d) none of these

Başlık: Ynt: Cubic polynomial
Gönderen: senior - Ocak 30, 2013, 01:24:20 öö

think about a = 1, b = 2, c = 2, d = 1
Then P(x) = x3 + 2x² + 2x + 1 = x²(x+1) + (x+1)² = (x+1)(x²+x+1)
which has roots x = -1, and two imaginary ones.
This holds with the condition but with none of choices a,b, or c. So, choice d.

Başlık: Ynt: Cubic polynomial
Gönderen: stuart clark - Şubat 04, 2013, 04:38:40 ös

Thanks Moderator Got it