NCERT Chapter Summary: Quadratic Equations

One type of polynomial is the quadratic polynomial of the form ax2 + bx + c, a ≠ 0. When you equate this polynomial to zero, you get a quadratic equation. Quadratic equations come up when you deal with many real-life situations.

quadratic equation in the variable x is of the form ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. A real number α is said to be a root of the quadratic equation ax2 + bx + c = 0, if aα2 + bα + c = 0.

The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same. If we can factorise ax2 + bx + c, a ≠ 0, into a product of two linear factors, then the roots of the quadratic equation ax2 + bx + c = 0 can be found by equating each factor to zero.

A quadratic equation can also be solved by the method of completing the square.

Quadratic formula: The roots of a quadratic equation ax2 + bx + c = 0 are given by the quadratic formula.

provided b2 - 4ac ≥ 0

A quadratic equation ax2 + bx + c = 0 has:

  1. two distinct real roots, if b2 - 4ac > 0
  2. two equal roots (coincident roots), if b2 - 4ac = 0
  3. no real roots, if b2 - 4ac < 0