Page 7 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

Checkpoint - 2

1. 64x – 529 = 0
2
2
2. x – x – 12 = 0
3. x -2√3 x + 3=0
2
4. bcx + (b -ac)x - ab=0
2
2
x x
2
5. 5( ) - 4( )-1=0; x≠ -1
x+1 x+1

B. Completing the Square Method:

Step- I: First obtain the quadratic equation and Let the quadratic

2
equation be ax +bx+c=0, a ≠0.

Step- II: Make the coefficient of ² unity by dividing throughout by it if

b
c
it is not unity that is obtain x²+ x+ =0
a a
b
c
Step-III: Shift the constant term c/a on R.H.S. to get x²+ x= -
a a
b
Step-IV: Add the square of half of the coefficient of x. i.e., ( ) ² on both
2a

sides to obtain.

b b b c
x²+2 ( ) x+ ( ) ²= ( ) ²-
2a 2a 2a a

Step-V: Write LHS as the perfect square and simplify RHS to get

2
(x+ ) ²= b²-4ac
2a 4a²

Step-VI: Take square root of both sides to get x+ b = ±√ b²-4ac
2a 4a²

b
Step-VII: Obtain the values of x by shifting the constant term on
2a

R.H.S., i.e., =- b ±√ b²-4ac
2a 4a²

7