Our ncert solutions for Exercise 4.3 Class 10 maths 4. Quadratic Equations - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

Exercise 4.3 Class 10 maths 4. Quadratic Equations - ncert solutions - Toppers Study

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Exercise 4.3 Class 10 maths 4. Quadratic Equations - ncert solutions - Toppers Study

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Exercise 4.3 class 10 Mathematics Chapter 4. Quadratic Equations

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• Exercise 4.3 Class 10 Maths 4. Quadratic Equations - Ncert Solutions - Toppers Study
• Class 10 Ncert Solutions
• Solution Chapter 4. Quadratic Equations Class 10
• Solutions Class 10
• Chapter 4. Quadratic Equations Exercise 4.3 Class 10

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4. Quadratic Equations

| Exercise 4.3 |

Exercise 4.3 Class 10 maths 4. Quadratic Equations - ncert solutions - Toppers Study

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Exercise: 4.3  

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Q1. Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

(i)  2x² - 7x + 3 = 0

Solution: a = 2, b = -7, c = 3

Now checking for nature of roots,

D = b² - 4ac

D = (-7)² - 4 x 2 x 3

D = 49 - 24

D = 25

Hence D > 0

∴ There is two different and real roots

    2x² - 7x + 3 = 0

Dividing by a term 2 we get.

 Putting A term and B term into a²-2ab+b²

(ii) 2x² + x - 4 = 0;

Solution: 

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

Now checking for nature of roots,

D = b² - 4ac

D = (1)² - 4 x 2 x -4

D = 1 - (-32)

D = 1 + 32

D = 33

Hence D > 0

∴ There are two distinct and real roots

    2x² + x - 4 = 0

(iii)  4x² + 4√3x + 3 = 0

Solution: 

a =4, b = 4√3, c= 3 

D = b² - 4ac = (4√3)² - 4 x 4 x 3

= 48 - 48 = 0    

Here D = 0 

Therefore, There are two real and equal roots. 

   4x² + 4√3x + 3 = 0

⇒(2x)² + 2 . 2x. √3 + (√3)² = 0 

⇒(2x + √3)²= 0 

⇒ (2x + √3)^​ (2x + √3)^​ = 0 

⇒ 2x + √3 = 0, 2x + √3 = 0

​⇒  2x = - √3,  2x = - √3

⇒ x = √3/2, x = √3/2

(iv) 2x² + x + 4 = 0;

a = 2, b = 1, c = 4

Now checking for nature of roots,

D = b² - 4ac

D = (1)² - 4 x 2 x 4

D = 1 - 32

D = -31

Hence D < 0

∴ There is no real root.

∴ Solution cannot be made of  2x² + 1x + 4 = 0