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 = ½

 

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.