CHAPTER :- QUADRATIC EQUATIONS!!.....

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

In fact , any equation of the form p(x) = 0 , where p(x) is a polynomial of degree 2 , is a quadratic equation. But when we write the terms of p(x) in descending order of their degrees , then we get the standard form of the equation .

Therefore the standard / general form of quadratic equation is ax² + bx + c = 0 , a 0 and a , b , c are real numbers. In this equation , variable is 'x' and the degree of the equation is '2'.

If x =  satisfies the equation ax² + bx + c = 0 , then is known as the root of the quadratic equation.

The roots and zeroes of the quadratic equation ax² + bx + c = 0 , a ≠ 0 are same.

If the given quadratic equation ax² + bx + c = 0 , a ≠ 0 can be factorised into two linear factors, then its roots can be found by equating each factor equal to zero.

We can solve quadratic equation by completing the square.

The roots of the quadratic equation ax² + bx + c = 0 , a ≠ 0 can be found by using the following formula, if its discriminate (D = b² – 4c) is greater than or equal to zero.

x = - b  b2 – 4ac / 2a

A quadratic equation ax² + bx + c = 0 , a ≠ 0 has:-

1. two distinct real roots , if D > 0.

2. two equal roots (i.e., repeated roots), if D = 0.

3. no real roots. if D < 0.

Questions related to this chapter will be posted soon!!..