Formula

Quadratic formula

Algebra • Quadratic Equations • Roots

Formula

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

For

a x^{2} + b x + c = 0

with

a \neq = 0

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

How to use it

1Use when factorisation is not obvious.
2The discriminant $D = b^{2} - 4 a c$ alone decides the nature of the roots: $D > 0$ real distinct, $D = 0$ equal, $D < 0$ non-real.
3Many questions ask only about $D$ and need no root computation at all.

Solve

x^{2} - 5 x + 6 = 0

Step-by-step

1
$a = 1, b = - 5, c = 6 \Rightarrow D = 25 - 24 = 1$
Why: Compute the discriminant first.
2
$x = \frac{5 \pm 1}{2}$
3
$x = 3$ or $x = 2$

Answer

x = 2, 3

Watch out

Requires

a \neq = 0

. If

a = 0

the equation is linear and the formula divides by zero.

Also known as

shreedharacharya formula, roots of a quadratic, discriminant