Quadratic Equation

An equation of the form ax2 + bx + c = 0, where a, b, c ∈ R and a ≠ 0, is called a quadratic equation.

Discriminant

The expression, D = (b2 − 4ac) is called the discriminant.

Roots of quadratic equation

Roots of ax2 + bx + c = 0 is given by :

α = − b + √D2a

β = − b − √D2a

If α, β are roots of ax2 + bx + c = 0, then

(α + β) = − ba

(αβ) = ca

Nature of roots

If D < 0, the given equation has no real roots.

If D = 0, the roots are real and equal, each equal to − b2a

If D > 0 and D is a perfect square, then the roots are rational and unequal.

If D > 0 and D is not a perfect square, then the roots are irrational and unequal.