Dr Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)

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Solutions to Chow Wai Keung’s Discovering Additional Mathematics (Textbook) Note that the tables have been slightly modified to include more information. Class Activity 1: p. 4 1.

Equation Remarks And So? Roots

(a) 1 4 3 ( )( )

implies that the equation has two real and distinct roots

( )( )

Roots: and

(b) 2 ( ) ( )( )

implies that the equation has two real and distinct roots

( )( )

Roots:

and

(c) 1 9 ( ) ( )( )

implies that the equation has two real and equal roots

( )( )

Roots: and

(d) 4 25 ( ) ( )( )

implies that the equation has two real and equal roots

( )( )

Roots:

and

(e) 1 5 7 ( )( ) implies that the equation has no

Dr Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)

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real roots

(f) 3 8 ( ) ( )( )

implies that the equation has no real roots

2. (a) Discriminant, is positive two real and distinct roots (b) Discriminant, is zero two real and equal roots (c) Discriminant, is negative no real roots Class Activity 2: p. 8 3.

Equation Remarks And So? Number of points of intersection with the -

axis

(a) 1 1 ( ) ( )( )

implies that the equation has two real and equal roots

Dr Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)

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(b) 2 10 7 ( )( )

implies that the equation has two real and distinct roots

(c) 1 10 ( ) ( )( )

implies that the equation has no real roots

(d) ( ) ( )( )

implies that the equation has two real and equal roots

(e) 7 ( )( )

implies that the equation has two real and distinct roots

(f) 10 ( )( )

implies that the equation has no real roots