Solve each of the following quadratic equations:
Given:
taking LCM; using (a + b)2 = a2 + b2 + 2ab
- 24x2 - 64x - 1 = 3(8x2 - 2x - 3) cross multiplying
- 24x2 - 64x - 1 = 24x2 - 6x - 9
48 x2 + 58x - 8 = 0 taking 2 common
24 x2 + 29x - 4 = 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 = 24 b = 29 c = - 4
= 24. - 4 = - 96
And either of their sum or difference = b
= 29
Thus the two terms are 32 and - 3
Difference = 32 - 3 = 29
Product = 32. - 3 = - 96
24 x2 + 29x - 4 = 0
24 x2 + 32x - 3x - 4 = 0
8x(3x + 4) - 1(3x + 4) = 0
(3x + 4)(8x - 1) = 0
(3x + 4) = 0 or (8x - 1) = 0
Hence the roots of equation are