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54

Solve each of the following quadratic equations:

taking LCM

3x^{2} + 2x - 1 = 14x - 10 cross multiplying

3x^{2} - 12x + 9 = 0 taking 3 common

x^{2} - 4x + 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 = 1 b = - 4 c = 3

= 1.3 = 3

And either of their sum or difference = b

= - 4

Thus the two terms are - 3 and - 1

Sum = - 3 - 1 = - 4

Product = - 3. - 1 = 3

x^{2} - 4x + 3 = 0

x^{2} - 3x - x + 3 = 0

x(x - 3) - 1(x - 3) = 0

(x - 3) (x - 1) = 0

(x - 3) = 0 or (x - 1) = 0

x = 3 or x = 1

Hence the roots of equation are 3 or1.