Solve each of the following quadratic equations:

√3x^{2} – 2√2x – 2√3 = 0

Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = √3 b = -2√2 c = -2√3

= √3.-2√3 = -2.3 = -6

And either of their sum or difference = b

= -2√2

Thus the two terms are -3√2 and √2

Difference = -3√2 + √2 = -2√2

Product = -3√2 × √2 = -3.2 = -6

(On using3√2 = √3 √3 √2 = √3.√6)

(∵2√3 = √2 √2 √3 = √2.√6)

Roots of equation are

27