Quadratic equation construction

Concept Video

Any Time Online Quiz

Certainly, Dr. E. Ramanathan! Below, you’ll find 20 multiple-choice questions related to the construction of quadratic equations, suitable for grade 10 mathematics.

1. If the roots of the quadratic equation are 4 and -2, what is the equation?
a)
b)
c)
d)

2. What is the quadratic equation if one root is 3 and the other root is the opposite of the first?
a)
b)
c)
d)

3. The sum of the roots of a quadratic equation is -5, and the product is 6. What is the equation?
a)
b)
c)
d)

4. If one root of a quadratic equation is twice the other, and the sum of the roots is 0, what is the equation?
a)
b)
c)
d)

5. The roots of the quadratic equation are 2 and 3. What is the value of b?
a) -5
b) 5
c) 6
d) -6

6. What are the roots of the quadratic equation ?
a) -2, 2
b) -4, 1
c) -2, -2
d) 4, -4

7. The value of one root of the equation is 1. What could be the value of k?
a) -4
b) 4
c) 2
d) 0

8. Which of the following cannot be a root of a quadratic equation with integer coefficients?
a) -1/2
b) 1/3
c) 3/4
d) 2/5

9. If one root of the equation is 5, what is the other root?
a) -1
b) 1
c) 0
d) 3

10. If the roots of a quadratic equation are both negative, what must be true?
a) The coefficient of is positive
b) The coefficient of is negative
c) The coefficient of is positive
d) The coefficient of is negative

11. The roots of the equation are:
a) 1 and 4
b) 1 and 3
c) 3 and 1
d) 3 and -3

12. What are the roots of the equation ?
a) 3, -3
b) -3, 3
c) 3, 3
d) 6, 0

13. If the roots of the equation are 1 and 5, what is the value of k?
a) -6
b) 6
c) -5
d) 5

14. What is the equation if the roots are the solutions to and ?
a)
b)
c)
d)

15. If the roots of a quadratic equation are 3 and 4, what is the value of the constant term?
a) 7
b) 12
c) -12
d) -7

16. What is the equation of the quadratic function that has roots at x = -2 and x = 1?
a)
b)
c)
d)

17. What is the sum of the roots of the equation ?
a) 10
b) -10
c) 7
d) -7

18. The quadratic equation has one root at 3. What could be the value of k?
a) 7
b) -7
c) 10
d) -10

19. If a quadratic equation has roots that are reciprocals of each other, what must be true about the equation?
a) The coefficient of is 0
b) The constant term is 1
c) The coefficient of is 1
d) The constant term is 0

20. If the roots of the quadratic equation are -1 and 2, what is the sum of the coefficients of the equation?
a) -1
b) 0
c) 1
d) 2

Key

1. b)
2. d)
3. a)
4. b)
5. b) 5
6. c) -2, -2
7. c) 2
8. d) 2/5
9. b) 1
10. c) The coefficient of is positive
11. b) 1 and 3
12. c) 3, 3
13. a) -6
14. d)
15. c) -12
16. c)
17. c) 7
18. a) 7
19. d) The constant term is 0
20. d) 2