Asked by Diana
Find all integers b so that the trinomial 3x^2 +bx + 2 can be factored.
Answers
Answered by
Steve
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^2-5x+2 = (3x-2)(x-1)
3x^2+5x+2 = (3x+2)(x+1)
3x^2-7x+2 = (3x-1)(x-2)
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.
so, b^2 - 24 > 0
b must be an integer such that |b| >= 5
3x^2-5x+2 = (3x-2)(x-1)
3x^2+5x+2 = (3x+2)(x+1)
3x^2-7x+2 = (3x-1)(x-2)
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.