Question

Any example of completing square method for 10 std

Answer 1

1) Find the roots of the equation 9x 2 - 15x + 6 = 0 using completing square method.

Solution :  

9x 2 - 15x + 6 = 0

9x 2 - 15x = - 6  

Here, leading coefficient = a = 9 , b = -15 and c = 6

Divide the whole equation by 9, we get

x 2 - 15x/9 = - 6/9  

x 2 - 5x/3 = - 2/3  

Now add (-b/2a) 2 = -[-5/(2 x 3)] 2 = (5/6) 2 both sides  

x 2 - 5x/3 + (5/6) 2 = -2/3 + (5/6) 2  

( x - 5/6) 2 = -2/3 + 25/36

( x - 5/6) 2 = (-24 + 25)/36

( x - 5/6) 2 = 1/36  

x - 5/6 = ~+mn~ 1/6  

∴ x = 5/6 ~+mn~ 1/6

x = 5/6 + 1/6 or x = 5/6 - 1/6

x = 6/6 = 1 or x = 4/6 = 2/3

So, roots of the equation are 1 and 2/3.