1.

Check whether the equation 6x2 – 7x + 2 = 0 has real roots, and if it has, find them by the method of completing the squares.

Answer»

The discriminant = b2 – 4ac

= 49 – 4 × 6 × 2

= 1 > 0

So, the given equation has two distinct real roots.

Now, 6x2 – 7x + 2 = 0

i.e., 36x2 – 42x + 12 = 0

i.e., 6x - (7/2)2+ 12 - 49/4 = 0

i.e., 6x - (7/2)2- (1/2)2= 0

or (6x - 7/2)2= (1/2)2

The roots are given by 6x - 7/2 = ±1/2

i.e., 6x = 4, 3

i.e., x = 2/3, 1/2.


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