The Discriminant - Algebra Step by Step

The discriminant b²-4ac of ax²+bx+c=0 determines the number of real roots: positive means two real roots, zero means one repeated root, negative means no real roots.

Example

Compute D=b squared minus 4ac and use its sign to classify the roots.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

x^{2} - 5x + 4 = 0

Step 2 — Compute D

Compute the discriminant: 25 - 16 = 9.

D= 25 - 16 = \hl{9}

Step 3 — Compare to zero

Compare D to zero: 9 > 0.

D= \hl{9} > 0

Step 4 — Classification

State the discriminant verdict.

\hl{two real roots}

discriminant Compute disc=b²-4ac. Its sign classifies the quadratic before solving: two real roots (disc>0), one repeated (disc=0), or no real roots (disc<0).