**Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.3 Q1 Download this solution**

#### 1. Find the roots of the following quadratic equations if they exist by the method of completing square.

#### (i)

#### (ii)

#### (iii)

#### (iv)

**Solution (i)**

#### First we divide equation by 2 to make coefficient of equal to 1, we get

#### We divide middle term of the equation by , we get

#### We add and subtract square of from the equation , we get

#### {}

#### Taking Square root on both sides, we get

#### And

#### Therefore,

#### Solution (ii)

#### Dividing equation by 2, we get

#### Following procedure of completing square, we get

#### {}

#### Taking square root on both sides, we get

#### And,

#### Therefore,

**Solution (iii)**

#### Dividing equation by 4 to make coefficient of equal to 1, we get

#### Following the procedure of completing square, we get

#### {}

#### Taking square root on both sides, we get

#### Quadratic equation has two roots. Here, both the roots have equal value. Therefore, value of

#### Solution (iv)

#### Dividing equation by 2 to make coefficient of equal to 1.

#### Following the procedure of completing square, we get

#### {}

#### Taking square root on both sides, right hand side does not exist because square root of negative number does not exist.

#### Therefore, there is no solution for quadratic equation