Thread: [SOLVED] Prove the existence of quadratic roots

If ab>0 and bc<0, then ax^2+bx+c=0 has two real solutions. (Prove this)

I started, but I don't know.

Let a, b, c be real.
Assume ab>0 and bc<0.
So bc<ab
So c>a.
So....

I don't know from here. It clearly involves showing that the discriminant, b^2-4ac is positive I would think. How I can go about doing so, not sure.

Thanks for the help.

ab > 0 and bc < 0

case 1 ...

a and b both > 0 ... then c < 0

then ac < 0, -4ac > 0

b^2 - 4ac > 0 ... two distinct real roots

case 2 ...

a and b both < 0 ... then c > 0

ac < 0 , -4ac > 0

b^2 - 4ac > 0 ... two distinct real roots