Ncert Solutions For Class 10 Maths Ex 4.3

Ncert Solutions For Class 10 Maths Chapter 4 Ex 4.3

Q.1 Find the roots of the equation 25x2 + 20x – 13 = 0 by method of completing the square.

Sol.

(5x)2 + 20x  = 13

(5x)2 + 2(5x.2)+ 22 = 13+22

(5x+2)2 – 17 = 0

Therefore  (5x+2)2(17)2=0

(5x+2+17)   (5x+217)=0

Therefore     x=2+175   or   x=2+175

 

Q.2 Find the roots of the equation 9x2 + 12x – 5 = 0 by method of completing the square.

Sol.

9x2 + 12x = 5

(3x)2 + 2(3x.2) = 5

(3x)2 + 2(3x.2) + 22 = 5 + 22

(3x+2)2 = 9

(3x+2)2 – 32 = 0

(3x + 2 + 3) (3x + 2 – 3) = 0

(3x + 5) (3x – 1) = 0

Therefore   x=53   or   x=13

 

Q.3 Find the roots of the equation 3x2 – 16x + 5 = 0 by method of completing the square.

Sol.

To solve the above equation either divide the entire equation by 3 to make 3x2 a perfect square but it will be much easier to solve the equation if we multiply the above equation by 3 to make 3x2 a perfect square.

Therefore,           9x2 – 48x = -15

(3x)2 – 2(3x.8) =-15

(3x)2 – 2( 3x.8 ) + 82 = -15 + 82

(3x – 8)2 – 49 = 0

(3x-8)2 – 72 = 0

(3x-8+7)(3x-8-7)=0

(3x-1)(3x-15)=0

Therefore       x=13   or   x=5

 

Q.4 Find the roots of the equation 2x2 + x – 4 = 0 by method of completing the square.

Sol.

Now, for making 2x2 a perfect square, multiplying the above equation by 2

Therefore,

4x2 + 2x = 8

Now,

(2x)2+2(2x.12)=8

 

(2x)2+2(2x.12)+14=8+14

 

(2x+12)2(334)2=0

 

(2x+12+332)(2x+12332)=0

 

Therefore   x=1+334  or  x=1+334

 

 

Consider a quadratic equation:

ax2 + bx+ c = 0 with a ≠ 0

The roots of the following quadratic equation are given by:

 

x=b+b24ac2a  and  x=bb24ac2a

 

(or)      x=b±b24ac2a

This is known as quadratic formulae for finding roots of quadratic equation.

Nature of roots:

The term (b2 – 4ac) is known as discriminant and it determines the nature of roots of the quadratic equation.

 

If b2 – 4ac > 0, then the equation will have two distant real roots.

 

If b2 – 4ac = 0, then the equation will have two equal real roots.

 

If b2 – 4ac < 0, then the equation will have unreal roots.