Quadratic Inequalities

Lesson · Intermediate

Algebra: Inequalities

f(x)=ax^2+bx+c, \qquad \Delta=b^2-4ac

Condition	Number of Real Roots	Sign of $f(x)$
$\Delta>0$	2	$\operatorname{sign}(a)\quad 0_{\,r_1}\quad -\operatorname{sign}(a)\quad 0_{\,r_2}\quad \operatorname{sign}(a)$
$\Delta=0$	1	$\operatorname{sign}(a)\quad 0_{\,r}\quad \operatorname{sign}(a)$
$\Delta<0$	0	$\operatorname{sign}(a)$