Q. 584.4( 7 Votes )

Solve each of the following quadratic equations:


Answer :

Given:

taking LCM


using (a - b)2 = a2 + b2 - 2ab


cross multiplying


18x2 - 48x + 130 = 105x - 140


18x2 - 153x + 270 = 0 taking 9 common


2x2 - 17x + 30 = 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 = 2 b = - 17 c = 30


= 2.30 = 60


And either of their sum or difference = b


= - 17


Thus the two terms are - 12 and - 5


Sum = - 12 - 5 = - 17


Product = - 12. - 5 = 60


2x2 - 17x + 30 = 0


2x2 - 12x - 5x + 30 = 0


2x(x - 6) - 5(x - 6) = 0


(x - 6) (2x - 5) = 0


(x - 6) = 0 or (2x - 5) = 0



Hence the roots of equation are


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