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Quadratic Equations

The general form of a quadratic equation is, where and .

Solving a quadratic equation by the method of completion of squares (SREEDHARACHARYA’S RULE)

$Quadratic equation$ Consider the quadratic equation

Dividing through out by a

Adding i.e.[½coeff. of x ]²

Taking square root on both sides and assuming ,

or

Thus, if , then the quadratic equation has two roots and , given by

and

Nature of the roots of a quadratic equation

Let where and be a quadratic equation, then

is called the discriminant of the equation.

I) If D>0, then there are two real and distinct roots, given by

and

II) If D=0, then the roots are real and equal, each being equal to –b/2a.

i.e.

III) If D<0, then there are no real roots.