Summary

In this chapter, you have studied the following points:

1. A quadratic equation in the variable x is of the form ax2 + bx +c = 0 , where a, b, c are real numbers and a≠=0.

2. A real number α is said to be a root of the quadratic equation ax2 + bx + c = 0 . The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 +bx +c = 0 are the samedifferent.

3. If we can factorise ax2 +bx +c = 0, 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 zeroone.

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

x=−b±b2−4ac2a, provided b2−4ac≥0.

5. A quadratic equation ax2 +bx +c = 0 has

(i) two distinct real roots, if b2-4ac ><0,

(ii) two equal real roots, if b2 - 4ac =≠ 0,

(iii)no real roots, if b2 - 4ac <>0.