Quadratic Equation 2012

Quadratic Equation_2011 Form 4

1. A quadratic equation

has no real roots. Find the range of values of . [3 marks]

2. Given

and are the roots of the quadratic equation constant. Find (a)

the value of

(b)

the value of

, where

such that

[3 marks]

3. Given

and are the roots of the quadratic equation are constants. Find the value of and of .

, where and [3 marks]

4. It is given that

and

is one of the roots of the quadratic equation are constants. Express in terms of .

5. Given that the roots of quadratic equation

(a)

the value of

(b)

is

, where [2 marks] are -3 and 4. Find

the value of

[3 marks]

6. It is given that

and are the roots of the quadratic equation quadratic equation with roots and .

. Form a [4 marks]

7. The quadratic equation

roots. If

and

, where and are constants, has equal are positive, find the ratio in the simplest form. [3 marks]

8. Solve the quadratic equation

significant figures. 9. Find the value of

. Give your answers correct to four [3 marks]

where the curve

touches the x-axis at only one [3 marks]

point. 10. Given

(a)

and are roots of the quadratic equation the value of (b) the value of

11. It is given that

is one of the roots of the quadratic equation

value of . 12. It is given that

value of

and and of .

are the roots of the quadratic equation

Prepared by : Puan Hayati Aini Ahmad

23 January 2012

, find [3 marks] . Find the [2 marks] . State the [3 marks]

Page 1

Quadratic Equation_2011 Form 4

13. The quadratic equation

, where

is a constant, has two different [3 marks]

roots. Find the range of values of . 14. Given the equation

has two distinct roots, find the range of values of [3 marks]

15. The quadratic equation

, where

range of values of . 16. Solve the quadratic equation

is a constant, has no roots. Find the [3 marks] . Give your answers correct to three [3 marks]

decimal places. 17. Given that

(a)

is one of the roots of the quadratic equation the value of (b) the other root of the equation

18. The quadratic equation

, where

is a constant, has two equal

roots. Find the values of .

[3 marks]

19. Form the quadratic equation which has the roots

of

, where

20. Find the range of values of

. Find [3 marks]

and

and

. Give our answer in the form

are constants.

if

Prepared by : Puan Hayati Aini Ahmad

has two different roots.

23 January 2012

[2 marks] [3 marks]

Page 2

Quadratic Equation_2011 Form 4

Answer Section 1. ANS:

2. ANS: (a)

(b)

3. ANS: , 4. ANS:

5. ANS: (a)

(b)

6. ANS:

;

Prepared by : Puan Hayati Aini Ahmad

23 January 2012

Page 3

Quadratic Equation_2011 Form 4

7. ANS:

8. ANS:

9. ANS:

10. ANS: (a)

(b)

11. ANS:

12. ANS: ; 13. ANS: Prepared by : Puan Hayati Aini Ahmad

23 January 2012

Page 4

Quadratic Equation_2011 Form 4

14. ANS:

15. ANS:

16. ANS:

17. ANS: (a)

(b)

18. ANS:

19. ANS:

20. ANS:

Prepared by : Puan Hayati Aini Ahmad

23 January 2012

Page 5

Quadratic Equation_2011 Form 4

Prepared by : Puan Hayati Aini Ahmad

23 January 2012

Page 6