The document discusses the nature of roots of a quadratic equation. It states that a quadratic equation generally has two roots, which can be real and distinct, real and coincident, or not real, depending on whether the discriminant (b^2 - 4ac) is positive, zero, or negative. The discriminant determines the type of roots and is an important property in solving quadratic equations.

1. QUADRATIC EQUATIONS

2. NATURE OF ROOTS OF A QUADRATIC
EQUATION
• Roots of the general quadratic equation
were obtained as,
This indicates that in general a quadratic
equation has two roots. But the nature of
these roots depends on the value of

3. • If is positive its square root is a real
non zero number and the equation will have
two real and unequal roots. In this case we say
that the roots of the quadratic equation are
real and distinct.

4. • If is zero we get only one solution,
For the equation and we say that the equation
has two coincident (or repeated) roots.
If is negative it has no real square roots
and we say that the roots of the equation are
not real.

5. • So we have,
• The converse of these are true.

6. • The expression is called the
discriminant of the equation and is denoted
by .
• From the above conditions we also have,