Question

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

Answer 1

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,\[b^2=12c=3 \times 4c\]

Answer 2

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?

Answer 3

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.

Answer 4

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

Answer 5

yes

Answer 6

gotcha, thanks a bunch!

Answer 7

No worries...become a fan ;)

Answer 8

already am!

Answer 9

Oh, good one!