Chapter 2 Quadratic Expressions and Equations (2) - 4C
Chapter 2 Quadratic Expressions and Equations (2) - 4C
Chapter 2 Quadratic Expressions and Equations (2) - 4C
___________
Sekolah Menengah Seri Omega
Teacher: WL Cheng
Class : 4C
Lesson No.:3
Date :13/1/09
Time :8.10-9.20
Subject: Mathematics
Chapter:2
Topic: Quadratic Expressions and Equations (2)
(b) ax2 + bx = 0,
where a 0, b 0 but c = 0,
e.g. 2x2 + 5x = 0
(c) ax2 + c = 0,
where a 0, c 0 but b = 0,
e.g. 3x2 + 7 = 0
Notes:1 Roots of a quadratic equation are values of
the unknown which satisfy the quadratic
equation.
2 To determine whether a given value of the
unknown is a root of a specific quadratic
equation, substitute the given value for the
unknown into the equation. If it satisfies the
equation, then the value of the unknown is a
root of the equation and vice versa.
3 Roots of an equation are also called the
solution of an equation. Therefore, in the
above example, x = - 1 and x = 1 are solutions
of the equation 3x2 + 4x + 1 = 0.
(b) p 2 6 p 7 0; p 7,0,1, 2
(e) 2d 3 8d 1 0
(a) x 2 x 1 0
(b) 3 y 5 6 y 1 0
(f) m m 1 0
(c) h 1 h 2 0
(g) 3q q 3 0
(d) 6 x 1 5 x 3 =0
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(h) x 5 x 0
(i) p 1 p 1 0
(c) m m 5 6 0
(j) y 13 =0
2
(d) y 2 5 y 6
(e) 2d 2 3d 0
3. Solve the following quadratic equations.
(a) x 6 x 2 2
(f) x 2 4 0
(b) p 2 3 p 4
(g) q 2 25
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(h) m 2 4m
(l) p 2 4 p 4 0
(i) 12 x 2 13 x 4
(m) 3 g 2 14 g 8 0
(j) 2 x 2 3 x 2 0
(n) 12m 2 7m 12 0
(k) 2 y 2 5 y 2 0
(o) 2 f 2 7 f 4 0
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(p) 5h 2 13h 6 0
(q) 6h 2 7 h 20
(s)
2x 7 x 6
3
3x 4
(t)
2x 1 5 x
x 3 2x 5
Answer
Exercise 2.4
1 (a) x = -4,3 :roots
x=0,2: not roots
(b) p = -7, 1 : roots
p = 0,2 : not roots
(r)
3
p
p 7 3p 5
2 (a) 2,-1
(b)
(c)-1,2
(d)
(e)
3 1
,
2 8
(g) 0,3
(i) 1,-1
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5
, 6
3
1 3
,
6 5
(f) 0,1
(h) 0, 5
(j) 13
3 (a)
1 2
,
2 3
(c) -1,6
(e) 0,
1 3
,
4 4
(g) -5,5
(i)
1 3
,
4 4
1
,2
2
2
(m) , 4
3
1
(o) , 4
2
4 5
(q) ,
3 2
1
(s) ,5
3
(k)
(b) -1, 4
(d) -1,6
(f) 2,-2
(h) 0,4
(j)
1
, 2
2
(l) 2
3 4
,
4 3
3
(p) , 2
5
(n)
(r) -3,5
(t) 2
Exercise
1. Write a quadratic equation for the area of the
following parallelogram.
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255338592.doc
Answer
4. -1 or 7
5.Breadth =
5
m, Length == 13 m
2
6. 11,12
7. 8, 15
8.. 6 seconds
9.. Breadth = 10 cm, Length == 15 cm
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