Find the roots of 6x2 – √2x – 2 = 0 by the factorisation of the

1.	Find the roots of 6x2 – √2x – 2 = 0 by the factorisation of the corresponding quadratic polynomial.
Answer» 6x² – √2x – 2 = 6x² – 3√2 x + 2√2 x – 2 = 3x (2x – √2 ) + √2 (2x – √2 ) = (3x + √2 ) (2x – √2) Now, 6x² – √2x – 2 = 0 gives (3x +√2 ) (2x –√2 ) = 0, i.e., 3x +√2 = 0 or 2x – √2 = 0 So, the roots are −√2/3 and √2/2.

Find the roots of 6x2 – √2x – 2 = 0 by the factorisation of the corresponding quadratic polynomial.

Answer»

6x² – √2x – 2

= 6x² – 3√2 x + 2√2 x – 2

= 3x (2x – √2 ) + √2 (2x – √2 )

= (3x + √2 ) (2x – √2)

Now, 6x² – √2x – 2 = 0 gives (3x +√2 ) (2x –√2 ) = 0, i.e., 3x +√2 = 0 or 2x – √2 = 0

So, the roots are −√2/3 and √2/2.