examday

/TMUA

The equation $ax^2+bx+c=0$, where $a,b,c$ are real and $a\ne0$, is said to have property R if it has two distinct real roots. Consider the following four statements.

• I. $b^2-4ac>0$ is necessary and sufficient for property R.
• II. $a$ and $c$ having opposite signs is a sufficient condition for property R.
• III. $a$ and $c$ having opposite signs is a necessary condition for property R.
• IV. $b\ne0$ is a necessary condition for property R.