Question

Find the roots of x 2 -4x-8 = 0 by the method of completing square.

Answer 1

Answer:

x = 2 ± 2√3

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

• The discriminant of the the quadratic equation

ax² + bx + c = 0 , is given as ; D = b² - 4ac

• If D > 0 then its roots are real and distinct.

• If D < 0 then its roots are imaginary.

• If D = 0 then its roots are real and equal.

Solution:

Here,

The given quadratic equation is :

x² - 4x - 8 = 0

Clearly, here we have ;

a = 1

b = -4

c = -8

Now,

The discriminant will be ;

=> D = b² - 4ac

=> D = (-4)² - 4•1•(-8)

=> D = 16 + 32

=> D = 48 (D > 0)

Since,

The discriminant of the given quadratic equation is greater than zero, thus there must exist two distinct real roots .

Now,

=> x² - 4x - 8 = 0

=> x² - 4x + 2² - 2² - 8 = 0

=> x² - 4x + 2² = 2² + 8

=> x² - 2•x•2 + 2² = 4 + 8

=> (x - 2)² = 12

=> x - 2 = √12

=> x - 2 = ± 2√3

=> x = 2 ± 2√3

Hence,

The roots of the given quadratic equation are :

x = 2 ± 2√3