Polynomials and Quadratic Theory

1. The diagram shows a cubic curve passing through (- 1, 0), (2, 0)and (0, - 8).

What is the equation of the curve?

A y=−2 ( x+1 )2(x+2)

B y=−2(x+1)(x−2)2

C y=4 (x+1)(x−2)

D y=−8(x+1)¿

2. 3 x2+12 x+17 is expressed in the form 3(x+ p)2+q.What is the value of q?

A 1

B 5

C 17

D −19

3. Calculate the discriminant of the quadratic equation 2 x2+4 x+5=0.

A −32

B −¿24

C 48

D 56

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Polynomials and Quadratic Theory - Continued

4. What is the remainder when x3+3 x2−5 x−6 is divided by ( x−2 )?

A 0

B 3

C 4

D 8

5. Solve 1−2 x−3 x2>0, where x is a real number.

A x←1, x>13

B −1<x<13

C x<13 , x>1

D −13

<x<1

6. The diagram shows a curve with equation of the formy=kx (x+a)2, which passes through the points (- 2, 0), (0, 0)and (1, 3).

What are the values of a and k?

A a=−2 and k=13

B a=−2 and k=3

C a=2 and k=13

D a=2 and k=3

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Polynomials and Quadratic Theory - Continued

7. If x2−6 x+14 is written in the form (x−p)2+q. What is the value of q?

A −¿22

B 5

C 14

D 50

8. A parabola intersects the axes at x=−2 and x=−1 and y=6, as shown in the diagram.

What is the equation of the parabola?

A y=6 (x−1 )(x−2)

B y=6 (x+1 )(x+2)

C y=3 ( x−1 )( x−2)

D y=3 ( x+1 )(x+2)

9. If x2−8 x+7 is written in the form (x− p)2+q. What is the value of q?

A −¿9

B −¿1

C 7

D 23

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Polynomials and Quadratic Theory - Continued

10. A function f ( x )=x3− x2+x+3 is defined on the set of real numbers. What is the remainder when f (x) is divided by ( x−1 )?

A 0

B 2

C 3

D 4

11. The discriminant of a quadratic is 23.

Here are two statements about this quadratic equation:

(1) the roots are real;(2) the roots are rational.

Which of the following is true?

A Neither statement is correct.

B Only statement (1) is correct.

C Only statement (2) is correct.

D Both statements are correct.

12. If f ( x )= (x−3 )(x+5), for what values of x is the graph of y=f (x ) above the x-axis?

A −5<x<3

B −3<x<5

C x←5, x>3

D x←3, x>5

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Polynomials and Quadratic Theory - Continued

13. The diagram shows the graph of a cubic.

What is the equation of this cubic?

A y=−x(x+1)(x−2)

B y=−x ( x−1 )(x+2)

C y=x (x+1)(x−2)

D y=x ( x−1 )(x+2)

14. Solve 6−x−x2<0.

A −3<x<2

B x←3, x>2

C −2<x<3

D x←2, x>3

15. When x2+8 x+3 is written in the form (x+ p)2+q. What is the value of q?

A −¿19

B −13

C −5

D 19

16. The roots of the equation kx2−3 x+2=0 are equal. What is the value of k?

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Polynomials and Quadratic Theory - Continued

A −98

B −89

C 89

D 98

17. The diagram shows the graph with equation y=k (x−1 )2(x+t ).

What are the values of k and t?

A k=−2 and t=−5

B k=−2 and t=5

C k=2 and t=−5

D k=2 and t=5

18. What is the solution of x2+4 x>0, where x is a real number?

A −4<x<0

B x←4, x>0

C 0<x<4

D x<0, x>4

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Polynomials and Quadratic Theory - Continued

19. Which of the following diagrams shows a parabola with equation y=a x2+bx+c. Where

a>0 b2−4 ac>0?

A

B

C

D

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Polynomials and Quadratic Theory - Continued

Answers

1. B 11. B

2. B 12. C

3. B 13. A

4. C 14. B

5. B 15. B

6. C 16. D

7. B 17. A

8. D 18. B

9. A 19. B

10. D

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