Transcript Quadratic Equations

Quadratic Equations
Solving by Factorisation
What is a Quadratic Equation?
Examples:
2x  9x  4  0
2
x  x  6
2
2x  4  0
2
x  6x  0
2
x  2  3x
2
What is a Quadratic Equation?
In general, a Quadratic Equation can be
simplified to the form
ax  bx  c  0
2
Where a, b and c are constants and a ≠ 0
Solving a Quadratic Equation
Methods of solving:



Factorisation
Completing the Square
Formula – (Sec 3)
Solving by Factorisation

Make sure one side of the equation is equal
to ZERO

Factorise (using either common factor/cross
method or both)

Apply Null Law

Find the unknowns
Null Law
When a × b = 0, either a = 0 or b = 0
As seen in Q1 (JiTT 3), null law can ONLY be
applied when one side of the equation is 0.
Example: Solve the equation
x  5x  6  0
( x  2)( x  3)  0
2
Applying null law,
either ( x  2)  0 or ( x  3)  0
 x  2 or x  3
This means that both values satisfies the
equation – both are the roots of the equation
Example: Solve the equation
2x  9x  0
2
x(2 x  9)  0
9
x  0 or 
2
Note: x(2x + 9) is same as (x − 0)(2x + 9)
Example: Solve the equation
9(2 x  1)  (5 x  4)
2
2
9(4 x  4 x  1)  25 x  40 x  16
2
2
36 x  36 x  9  25 x  40 x  16
2
2
11x  76 x  7  0
(11x  1)( x  7)  0
2
1
x  7 or 
11
Summary
A quadratic equation usually has 2 roots.
It is possible to get only 1 solution:
(x – 1)2 = 0  x = 1
But this just means the 2 roots are the same!
Therefore we can consider it as just 1 solution.