chapter 4 ii quadratic equations enrich
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4.1 Quadratic ExpressionA quadratic expression is an expression of the form ax2 + bx + c where a, b and c are
constants, a ≠ 0 and x is an unknown.
Factorisation of Quadratic Expressions using the cross method.
Quadratic Expressions and Equations
Example :
Factorise each of the following :
Exercise
1 x2 + 5x + 6 = (x + 2)(x + 3)
x 2 2x
x 3 3x
x2 +6 5x
(i) x2 + 7 x + 10
(ii) x2 + 6 x + 8
2 x2 – 7x + 12 = (x –3)(x – 4)
x –3 –3x
x – 4 – 4x
x2 +12 –7x
(i) x2 – 5x + 6
(ii) y2 – 8y + 15
1
CHAPTER 4
QUADRATIC EXPRESSIONS AND EQUATIONS
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Solution of Quadratic EquationsFirst, write the quadratic equation in the form ax2 + bx + c = 0 , a ≠ 0.
Then factorise and write in the form of (x + a)(x + b) = 0
Thus x + a = 0 or x + b = 0
And x = - a, x = - b.
Questions based on the examination format
1. Solve (f – 1)(f – 2) – 6 = 0
2. Solve the equation 15
32 2
=−
n
n
3. Solve the following equation
3m2
= 2(m-3) + 11.
4. Solve the equation )1(732−=+ y y
5. Solve the equation 26
32 2
=
+
−
m
mm
6. Solve the equation7
32 2+
=k
k .
7. Solve the equations ( ) p p 532
12−= .
8 . Solve the equationh
hh
35
2−
=− .
9. Solve equation ( ) 111
62 2
=+
n
n
10. Solve the equation
x2 - 3 x + 2 = 2( x - 1)
Past Year SPM Questions
1. November 2003
Solve the equation 3x2 = 2(x – 1) + 7.
2. July 2004
Solve the quadratic equation .224
3 2+=
p p
3. November 2004
Solve the equation.2
1
522
=
+
+
m
mm
4. July 2005
Solve the quadratic equation mm2
712
2−=− .
5. November 2005
Quadratic Expressions and Equations 2
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Solve the quadratic equation k k
33
522
=
−
.
6. July 2006
Solve the quadratic equation .21532 2 x x x +=+
7. November 2006
Solve the quadratic equation 62
)1(3+=
− x
x x
8. June 2007
Using factorization, solve the following quadratic equation 25 8 6 5 x x x+ = −
9. Nov 2007
Using factorization, solve the following quadratic equation 24 15 17 x x− = −
10. June 2008
Solve the quadratic equation2(2 1) 2 x x x+ = −
11 Nov 2008
Solve the quadratic equation6 3
12
x x
x
−− =
Quadratic Expressions and Equations 3
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ANSWERS
Questions based on examination format
1 f = -1, 4 2n =
2
1
−
, 33
m =3
5
, -14 y = 5, 2
5m =
2
3−, 4
6k =
2
1, -3
7P =
2
1, -3
8h =
2
1− , 3
9n =
2
3, 4
10 x = 1, 4
SPM Past Year Questions
11,
3
5−= x
22,
3
4−= p
32,
2
1−=m
42,
4
1−=m
55,
2
1−=k
63,
2
5−= x
73,
3
4−= x
8 2, 3
5
x = −
9 3, 5
4 x = −
10 2, 1
3 x = −
11 3, 2
2 x = −
Quadratic Expressions and Equations 4
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