mathematics in action 4A full soluion

1 Quadratic Equations in One Unknown (I)

Review Exercise 1 (p. 1.4)

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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)