Question

solve the following Quadratic equation by completing the square method ​

Answer 1

Step-by-step explanation:

Given 3x^2 −5x+2=0

Here, the coefficient of x^2 is 3 and it is not a perfect square.

∴ Multiply the equation throughout by 3.(3x^ 2−5x+2=0)×3

∴9x^2 −15x+6=0

Now, half of the coefficient of x is 5/2

.∴b= 5/2

and b^2 =(5/2)^2

So, 9x^2 −15x+(5/2)^2 −(5/2)^2 +6=0,

(3x)^2 −15x+(5/2 )^2 =(5/2 )^2−6

(3x−5/2)^2= 25/4 −6= 1/4

(Taking square root on both the sides)

∴3x− 5/2 =± 1/2

∴3x− 5/2 =± 1/2

or 3x− 5/2 =− 1/2

3x= 1/2+5/2

3x= 5/2−1/2

3x= 6/2=3 3x= 4/2=2

∴x=1 x= 2/3