Solve each of the following quadratic equations:
Given:
taking LCM
(3x + 4)(x + 4) = 5x2 + 15x + 10 cross multiplying
3x2 + 16x + 16 = 5x2 + 15x + 10
2x2 - x - 6 = 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 = - 1 c = - 6
= 2. - 6 = - 12
And either of their sum or difference = b
= - 1
Thus the two terms are - 4 and 3
Difference = - 4 + 3 = - 1
Product = - 4.3 = 12
2x2 - x - 6 = 0
2x2 - 4x + 3x - 6 = 0
2x(x - 2) + 3(x - 2) = 0
(x - 2) (2x + 3) = 0
(x - 2) = 0 or (2x + 3) = 0
Hence the roots of equation are