Question

Part E
Solve the equation x^2- 4x + 6 = 0 by completing the square.​

Answer 1

Answer:

Roots for the given polynomial p(x) is  x = (2 + √2i) or  x = (2 - √2i)

Step-by-step explanation:

Here, the given polynomial is$P(x) = x^{2}  - 4x + 6 = 0$

Now, in COMPLETING THE SQUARE there are various steps.

Step (1): HALF THE COEFFICIENT OF x

Here, the coefficient of x  =  (4) so , the half of 4 =  4/ 2  = 2

Step(2) :Square it ADD IT ON BOTH SIDES OF EQUATION

The square of 2 is $(2)^2$.

Adding it on both sides of the polynomial, we get

$P(x) :  x^{2}  - 4x + 6  + (2)^2 = 0   + (2)^2$

Step (3): Use the ALGEBRAIC IDENTITY and make a complete square.

Now, using the identity $(a\pm b)^2 = a^2 + b^2 \pm 2ab$

$\implies x^{2}  - 4x + 6  + (2)^2 = 0   + (2)^2\\=  (x^{2}  - 4x + (2)^2 )+ 6   = 0   + (2)^2\\= (x-2)^2   +  6  -  (2)^2 =  0\\\implies  (x-2)^2  + 2 = 0$

or, $(x-2)^2  =  -2$

Rooting both sides, we get

$\pm (x-2)  = (\sqrt2i)$

Solving this, further,we get

x = 2 + √2i , or x  =  x = 2 - √2i

Hence, roots for the given polynomial p(x) is  x = 2 + √2i or  x = 2 - √2i