(Q14)Find the roots of the following quadratic equation, if they exist by the method of completing the square.

(iii) 5x2 - 7x - 6 = 0

Answer:

Given quadratic equation = 5x2 - 7x - 6 = 0

∴ 5x2 - 7x - 6

x2 -
7
5
x =
6
5
, it can be re-written as x2 - 2.
7
10
x =
6
5
 now it is in the form of a2 -2ab where a = x, and b =
7
10
Now adding b2 = (
7
10
 )2 on both sides, we get
x2 - 2.
7
10
x + (
7
10
 )2 =
6
5
 + (
7
10
 )2

(x -
7
10
 )2 =
6
5
 +
49
100
 =
+
100
 =
100
 = (
10
 )2

x -
7
10
 = ±
10

x =
7
10
 ±
10
 =
7+
10
 ,
7-
10
=
10
 ,
-
10
= (,
-
5
 )

Note: If we take the quadratic equation as 5x2 - 7x + 6 = 0, then we get the T.B answer