anonymous
  • anonymous
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
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Well, a quadratic equation has only one real root when the discriminant is zero. That is, when\[\Delta =b^2-4.3.c=b^2-12c=0\]here.Add 12c to both sides,\[b^2=12c=3 \times 4c\]
anonymous
  • anonymous
so 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
  • anonymous
There'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.

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anonymous
  • anonymous
so the fact that b^2 = 12c, b also has to be even
anonymous
  • anonymous
yes
anonymous
  • anonymous
gotcha, thanks a bunch!
anonymous
  • anonymous
No worries...become a fan ;)
anonymous
  • anonymous
already am!
anonymous
  • anonymous
Oh, good one!

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