**Class ten Quadratic Equations NCERT Solutions**

**Chapter 4: Quadratic Equations**

**TEXTBOOK’S EXERCISE 4.3**

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

(i) 2x^{2} – 7x +
3 = 0

(ii) 2x^{2} + x – 4 = 0

(iv) 2x^{2} + x +
4 = 0

**Sol.
**(i) Given equation
is : 2x^{2} – 7x + 3 = 0

⇒ 2x^{2} –
7x = –3

Dividing both sides by 2, we get

⇒ x = 2/4 =1/2

Hence, the roots of a quadratic equation are 12 and 3.

(ii) Given equation is : 2x^{2} + x – 4 = 0

⇒ 2x^{2} + x = 4

Dividing both sides by 2, we get

Adding (1/4) ^{2} to both sides, we get

Hence, the roots of a quadratic equation are

Hence, the roots of the given quadratic equation are

(iv) Given equation is : 2x^{2} + x + 4 = 0

⇒ 2x^{2} + x = – 4

Dividing both sides by 2, we get

Adding (1/4)^{2} to both sides, we get

Since the square of any number cannot be negative. So,

cannot be negative for any real x.

∴ There is no real x which satisfies the given quadratic equation. Hence, given the quadratic equation has no real roots.

**2. **Find the roots of the quadratic equations given in
Q.1 above by applying the quadratic formula.

**Sol.
**(i) Given equation
is : 2x^{2} – 7x + 3 = 0

This is of the form ax^{2} + bx + c = 0

Where a = 2, b = –7, c = 3

Now, b^{2} – 4ac = (–7)^{2} – 4 × 2 × 3 = 49 – 24 = 25

= 12/4 and 2/4 = 3 and 1/2

Hence, 3 and 1/2 are the roots of given quadratic equation.

(ii) Given equation is : 2x^{2} + x – 4 = 0

This is of the form ax^{2} + bx + c = 0.

Where a = 2, b = 1, c = – 4

Now, b^{2} – 4ac = (1)^{2} – 4 × 2 × (– 4) = 1 + 32 = 33

are the roots of given quadratic equation.

are the roots of given quadratic equation.

(iv) Given equation is : 2x^{2} + x + 4 = 0

This is of the form ax^{2} + bx + c = 0.

Where, a = 2, b = 1, c = 4

Now, b^{2} – 4ac = (1)^{2} – 4 × 2 × 4 = 1
– 32

= –31 < 0

As, b^{2} – 4ac < 0, therefore the given quadratic equation will have no real roots.