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anonymous
 5 years ago
having trouble with this:
If b and c are integers such that the equation 3x^2 + bx + c = 0 has only one real root, which of the following statements must be true?
1: b is even
2: c is odd
3: b^2 is a multiple of 3
anonymous
 5 years ago
having trouble with this: If b and c are integers such that the equation 3x^2 + bx + c = 0 has only one real root, which of the following statements must be true? 1: b is even 2: c is odd 3: b^2 is a multiple of 3

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, a quadratic equation has only one real root when the discriminant is zero. That is, when\[\Delta =b^24.3.c=b^212c=0\]here.Add 12c to both sides,\[b^2=12c=3 \times 4c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the key here is to know that fact about the discriminant and then you solve for your variables? also, how do you know that b is even?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There's a theorem that says is a number squared is even, then the number itself is even. That is, if b^2 is even, then b is even.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the fact that b^2 = 12c, b also has to be even

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0gotcha, thanks a bunch!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No worries...become a fan ;)
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