mathematics in action 4A full soluion
1 Quadratic Equations in One Unknown (I)
Review Exercise 1 (p. 1.4)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Let’s Discuss
Let’s Discuss (p. 1.23)
Angel’s method:
Using the quadratic formula,
Ken’s method:
Using the quadratic formula,
Let’s Discuss (p. 1.30)
The solution obtained by using the factor method is the exact value of the root. However, the solution obtained by using the graphical method is an approximation only.
Classwork
Classwork (p. 1.8)
(a)
Integer
(b)
Natural number
(c)
Negative integer
(d)
Terminating decimal
(e)
Recurring decimal
(f)
Fraction
(g)
Irrational number
Classwork (p. 1.11)
1.
(a) When x = 3, L.H.S. == 0 R.H.S. = 0 Since L.H.S. = R.H.S., 3 is a root of the equation.
(b) When x = 6, L.H.S. == 9 R.H.S. = 0 Since L.H.S. R.H.S., 6 is not a root of the equation. (c) When x = –3 , L.H.S. == 36 R.H.S. = 0 Since L.H.S. R.H.S., –3 is not a root of the equation.
2. (a) When x = –4, L.H.S. == 0 R.H.S. = 0 Since L.H.S. = R.H.S., –4 is a root of the equation. (b) When, L.H.S. = R.H.S. = 0 Since L.H.S. R.H.S., is not a root of the equation. (c) When, L.H.S. = R.H.S. = 0 Since L.H.S. = R.H.S., is a root of the equation.
Classwork (p. 1.26)
(a) The x-intercepts of the graph are
(b) The roots of the equationare
Quick Practice
Quick Practice 1.1 (p. 1.6)
(a)
∴
(b)
∴
(c)
∴
Quick Practice 1.2 (p. 1.10)
(a)
∴
(b) ∴
(c) ∴
(d) ∴
Quick Practice 1.3 (p. 1.13)
(a)
(b)
(c)
Quick Practice 1.4 (p. 1.14)
(a)
(b)
Quick Practice 1.5 (p. 1.15)
(a)
∴
(b) ∴ x = –4
Quick Practice 1.6 (p. 1.16)
(a)
(b)
Quick Practice 1.7 (p. 1.21)
(a) Using the quadratic formula,
(b) Using the quadratic formula,
(c) Using the quadratic formula, ∵ is not a real number. ∴ The equation has no real roots.
Quick Practice 1.8 (p. 1.21)
(a)
Review Exercise 1 (p. 1.4)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Let’s Discuss
Let’s Discuss (p. 1.23)
Angel’s method:
Using the quadratic formula,
Ken’s method:
Using the quadratic formula,
Let’s Discuss (p. 1.30)
The solution obtained by using the factor method is the exact value of the root. However, the solution obtained by using the graphical method is an approximation only.
Classwork
Classwork (p. 1.8)
(a)
Integer
(b)
Natural number
(c)
Negative integer
(d)
Terminating decimal
(e)
Recurring decimal
(f)
Fraction
(g)
Irrational number
Classwork (p. 1.11)
1.
(a) When x = 3, L.H.S. == 0 R.H.S. = 0 Since L.H.S. = R.H.S., 3 is a root of the equation.
(b) When x = 6, L.H.S. == 9 R.H.S. = 0 Since L.H.S. R.H.S., 6 is not a root of the equation. (c) When x = –3 , L.H.S. == 36 R.H.S. = 0 Since L.H.S. R.H.S., –3 is not a root of the equation.
2. (a) When x = –4, L.H.S. == 0 R.H.S. = 0 Since L.H.S. = R.H.S., –4 is a root of the equation. (b) When, L.H.S. = R.H.S. = 0 Since L.H.S. R.H.S., is not a root of the equation. (c) When, L.H.S. = R.H.S. = 0 Since L.H.S. = R.H.S., is a root of the equation.
Classwork (p. 1.26)
(a) The x-intercepts of the graph are
(b) The roots of the equationare
Quick Practice
Quick Practice 1.1 (p. 1.6)
(a)
∴
(b)
∴
(c)
∴
Quick Practice 1.2 (p. 1.10)
(a)
∴
(b) ∴
(c) ∴
(d) ∴
Quick Practice 1.3 (p. 1.13)
(a)
(b)
(c)
Quick Practice 1.4 (p. 1.14)
(a)
(b)
Quick Practice 1.5 (p. 1.15)
(a)
∴
(b) ∴ x = –4
Quick Practice 1.6 (p. 1.16)
(a)
(b)
Quick Practice 1.7 (p. 1.21)
(a) Using the quadratic formula,
(b) Using the quadratic formula,
(c) Using the quadratic formula, ∵ is not a real number. ∴ The equation has no real roots.
Quick Practice 1.8 (p. 1.21)
(a)