Posted by Diana on Saturday, February 11, 2012 at 4:06pm.
Find all integers b so that the trinomial 3x^2 +bx + 2 can be factored.

algebra  Steve, Saturday, February 11, 2012 at 6:18pm
The discriminant must be positive for there to be real roots, that is, factors
so, b^2  24 > 0
b must be an integer such that b >= 5
3x^25x+2 = (3x2)(x1)
3x^2+5x+2 = (3x+2)(x+1)
3x^27x+2 = (3x1)(x2)
3x^2+7x+2 = (3x+1)(x+2)
Many others are possible, not all of which factor into rational roots. Any integer b > 5 will provide real roots, however.
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