Cambridge Additional Mathematics

66 Quadratics (Chapter 3)

SOLVING BY FACTORISATION

Step 1: If necessary, rearrange the equation so one side is zero.

Step 2: Fully factorise the other side.

Step 3: Apply the rule: If ab=0then a=0or b=0.

Step 4: Solve the resulting linear equations.

Example 1 Self Tutor

Solve forx:

a 3 x^2 +5x=0 b x^2 =5x+6

a 3 x^2 +5x=0

) x(3x+5)=0

) x=0or 3 x+5=0

) x=0or x=¡^53

b x^2 =5x+6

) x^2 ¡ 5 x¡6=0

) (x¡6)(x+1)=0

) x=6or¡ 1

Example 2 Self Tutor

Solve forx:

a 4 x^2 +1=4x b 6 x^2 =11x+10

a 4 x^2 +1=4x

) 4 x^2 ¡ 4 x+1=0

) (2x¡1)^2 =0

) x=^12

b 6 x^2 =11x+10

) 6 x^2 ¡ 11 x¡10 = 0

) (2x¡5)(3x+2)=0

) x=^52 or ¡^23

Caution:

² Do not be tempted to divide both sides by an expression involvingx.

If you do this then you may lose one of the solutions.

For example, consider x^2 =5x.

Correct solution

x^2 =5x

) x^2 ¡ 5 x=0

) x(x¡5) = 0

) x=0or 5

Incorrect solution

x^2 =5x

)

x^2

x

=

5 x

x

) x=5

By dividing both sides

byx, we lose the solution

x=0.

² Be careful when taking square roots of both sides of an equation. You may otherwise lose solutions.

For example:

I Consider x^2 =25.

Correct solution

x^2 =25

) x=§

p

25

) x=§ 5

Incorrect solution

x^2 =25

) x=

p

25

) x=5

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_03\066CamAdd_03.cdr Thursday, 3 April 2014 4:15:46 PM BRIAN