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NCERT Solutions for Class 10th Mathematics

 

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Chapter 4. Quadratic Equations

Exercise 4.3

 

 

 

Exercise: 4.3  


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

quadtratic Equation

(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 = (43)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

 

 

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