Preliminary Mathematics Worksheet
Quadratic Equations
NSW Syllabus Ref: 1.4

© Mathematics Plus, 2002


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1.    Solve these equations:

I

II

III

(a)

(x - 1)(x - 2) = 0

(a)

(x - 3)(x+ 2) = 0

(a)

2(x - 3)(x+ 2) = 0

(b)

x(x - 5) = 0

(b)

x(x + 5) = 0

(b)

2x(x - 5) = 0

(c)

(5 - x)(x - 4) = 0

(c)

(2 - x)(8 - x) = 0

(c)

(1 - x)(1 + x) = 0

(d)

(3x - 1)(2x - 2) = 0

(d)

3(6x + 5)(x - 2) = 0

(d)

3x(5 - 4x) = 0

(e)

(1 - x)2 = 0

(e)

(5x + 3)2 = 0

(e)

x(5 - 2x)2 = 0




2.    Solve these quadratic equations by factorising:

I

II

III

(a)

x2 - 3x + 2 = 0

(a)

x2 - 7x + 12 = 0

(a)

x2 - 2x - 3 = 0

(b)

x2 + 2x - 3 = 0

(b)

x2 - 3x - 10 = 0

(b)

x2 - 5x + 6 = 0

(c)

x2 - 9x - 10 = 0

(c)

x2 - 6x + 9 = 0

(c)

x2 - 4x + 4 = 0

(d)

3x2 + 8x + 4 = 0

(d)

3x2 + 2x - 1 = 0

(d)

6x2 - 13x + 6 = 0




3.    Solve these equations:

I

II

III

(a)

x2 + 2x - 3 = 0

(a)

x2 - 2x - 15 = 0

(a)

x2 - x - 2 = 0

(b)

x2 + 2x = 3

(b)

x2 - 2x = 15

(b)

x2 = x+ 2

(c)

2x2 + 3x + 1 = 0

(c)

2x2 - x - 1 = 0

(c)

4x2 - 4x - 3 = 0

(d)

2x2 + 3x = -1

(d)

2x2 = x + 1

(d)

4(x2 - 1) = 3




4.    Solve for x:

I

II

III

(a)

x2 - 3x = 0

(a)

x2 + 13x = 0

(a)

x2 = 5x

(b)

3x2 + 6x = 0

(b)

2x2 = x

(b)

3x = 2x2

(c)

2x2 = -x

(c)

2u2 + u = 0

(c)

2(x - 1)2 + (x - 1) = 0

(d)

x2 = 1

(d)

2x2 = 2

(d)

4x2 = 1

(e)

(x + 1)2 = 1

(e)

2(x + 1)2 = 2

(e)

4(x - 3)2 = 1




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