A quadratic equation is an equation where the highest power of x is x2. The standard form of quadratic equation is:

ax2 + bx + c = 0

Quadratic Formula

If α, β are roots of quadratic equation, then

Discriminant and Nature of Roots

D or Δ = b2 - 4ac

  • If Δ > 0 and perfect square, then roots are real, rational and distinct
  • If Δ > 0 and not perfect square, then roots are real, irrational and distinct
  • If Δ = 0, roots are real and equal
  • If Δ < 0, then roots are complex conjugate numbers

Sum and Product of Roots

When α and β are roots,

α + β = -b/a

αβ = c/a

Formation of quadratic equation with given roots, α and β

x2 - (α + β)x b+ αβ = 0

Limiting Values