Solve each of the following quadratic equations:
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