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Chapter 8: Quadratic Equations Exercise 8.4

Question: 1

By using the method of completing the square, find the roots of quadratic equations.



Solution:





So, the roots for the given equation are: x = 3√2or x = √2.

Question: 2

By using the method of completing the square, find the roots of quadratic equations.

2x2 − 7x + 3 = 0 

Solution:

2x2 - 7x + 3 = 0





x = 12/4 or x = 2/4  

x = 3 or x = 1/2

Question: 3

By using the method of completing the square, find the roots of quadratic equations.

3x2 + 11x + 10 = 0 

Solution:

3x2+ 11x + 10 = 0





x = (-5)/3 or x = - 2

Question: 4

By using the method of completing the square, find the roots of quadratic equations.

2x2 + x − 4 = 0

Solution:

2x2 + x − 4 = 0





Are the two roots of the given equation.

Question: 5

By using the method of completing the square, find the roots of quadratic equations.

2x2 + x + 4 = 0

Solution:

2x2 + x + 4 = 0 

x2 + x2 + 2 = 0



Since, √(-31)  is not a real number, Therefore, the equation doesn’t have real roots.

Question: 6

By using the method of completing the square, find the roots of quadratic equations.



Solution:



Therefore, x = (- √3)/2 and x = (- √3)/2. Are the real roots of the given equation.

Question: 7

By using the method of completing the square, find the roots of quadratic equations.



Solution:



Question: 8

By using the method of completing the square, find the roots of quadratic equations.



Solution:





Question: 9

By using the method of completing the square, find the roots of quadratic equations.



Solution:





x = √2  or  x = 1.

Question: 10

By using the method of completing the square, find the roots of quadratic equations.

x2 - 4ax + 4a2 - b2 = 0 

Solution:

 x2 - 4ax + 4a2 - b2 = 0

x2 - 2(2a).x + (2a)2 - b2 = 0

(x - 2a)2 = b2 x - 2a = ± b x - 2a = b or x - 2a

= - b x = 2a + b or  x = 2a - b

Therefore, x = 2a + b or  x = 2a - b are the two roots of the given equation.

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