## 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

1. 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,$b^2=12c=3 \times 4c$

2. 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?

3. 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.

4. anonymous

so the fact that b^2 = 12c, b also has to be even

5. anonymous

yes

6. anonymous

gotcha, thanks a bunch!

7. anonymous

No worries...become a fan ;)

8. anonymous