Page 8 - CHAPTER 4 (Quadratic equations)
P. 8
CHAPTER 4
QUADRATIC EQUATIONS
Try and learn
2
Example 6: 9x -15x+6=0
2
Solution: Here, 9x -15x+6=0
6
15
⇒ x²- x+ =0 [Dividing throughout by 9]
9 9
5 2
⇒x²- x+ =0
3 3
2
5
⇒x²- x=- [Shifting the constant term on RHS]
3 3
5
2
5
5
⇒x²-2 ( ) x+ ( ) ²= ( ) ²- [Adding square of half of coefficient of x on
6 6 6 3
both sides]
5 25 2 5 25-24 5 1
⇒ (x- ) ²= - ⇒ (x- ) ²= ⇒ (x- ) ²=
6 36 3 6 36 6 36
5
1
⇒ x- = ± [Taking square root of both sides]
6 6
5 1 5 1 5 1 4 2
⇒ x= ± ⇒ x= + =1 or, x= - = =
6 6 6 6 6 6 6 3
2
⇒ x=1 or, x=
3
Example 7: Solve the equation x²-(√3+ 1)x+ √3=0 by the method of
completing the square.
Solution: We have,
x²-(√3+ 1)x+ √3=0
⇒x²-(√3+ 1)x= - √3
√3+1 √3+1 √3+1
⇒x²-2 ( ) x+ ( ) ²= -√3+ ( ) ²
2 2 2
√3+1 -4√3+ (√3+ 1)²
⇒ (x- ) ²=
2 4
8
