Quadratic Equations & Inequalities

← Back to Mathematics

Number of Real Roots

Discriminant Roots
$b^2 - 4ac > 0$2 real and distinct roots
$b^2 - 4ac = 0$1 real root (2 real and equal roots)
$b^2 - 4ac < 0$0 real roots
Has real roots: $b^2 - 4ac \geq 0$

Line & Curve

Discriminant Intersection
$b^2 - 4ac > 0$Intersects at 2 points
$b^2 - 4ac = 0$Tangent
$b^2 - 4ac < 0$Does not intersect
Line meets curve: $b^2 - 4ac \geq 0$

Curve Always Positive/Negative

$b^2 - 4ac < 0$ (curve has no real roots)
Curve always positive: $a > 0$
Curve always negative: $a < 0$
Next
Indices & Surds