**Determining the nature of roots of Quadratic equation:**

**Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Q1 Download this solution**

**1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.**

(i)

(ii)

(iii)

**Solution (i)**

Comparing this equation with general equation , we get

and .

** **

**Discriminant is less than 0 which means equation has no real roots.**

**Solution (ii)**

Comparing this equation with general equation , we get and c=4.

Discriminant =

Discriminant is equal to zero which means equations has equal real roots.

**Applying quadratic formula** to find roots we get,

Because, equation has two equal roots, it means .

is also equal to . Therefore

**Solution (iii)**

Comparing equation with general equation , we get

, and .

**Discriminant =**

Value of discriminant is greater than zero. Therefore, equation has distinct and real roots.

**Applying quadratic formula** to find roots we get,