Exercises for Question Type 3: Finding how many roots the quadratic has

Question 1

Skill question

Find the number of real roots of the quadratic $x^{2} - 4 x + 4 = 0$ .

[3]

Question 2

Skill question

How many real roots does the quadratic equation $x^{2} + 2 x + 5 = 0$ have?

[3]

Question 3

Skill question

Find the value of $k$ such that the quadratic equation $k x^{2} + 2 x + 1 = 0$ has exactly one real root.

[3]

Question 4

Skill question

Determine the number of real solutions of $2 x^{2} - 8 x + 6 = 0$ .

[3]

Question 5

Skill question

Determine the range of values of $k$ for which the equation $k x^{2} + 2 x + 1 = 0$ has two distinct real roots.

[6]

Question 6

Skill question

How many real solutions does $4 x^{2} - 4 x + 1 = 0$ have?

[3]

Question 7

Skill question

Find how many real roots the quadratic $3 x^{2} + 6 x + 2 = 0$ has.

[3]

Question 8

Skill question

Determine the number of real roots of the quadratic equation $6 x^{2} - 5 x + 105 = 0$ .

[3]

Question 9

Skill question

Find the number of real roots of the quadratic $7 x^{2} + 14 x + 7 = 0$ .

[3]

Question 10

Skill question

Determine how many real roots the equation $10 x^{2} + 3 x - 1 = 0$ has.

[3]

Question 11

Skill question

Determine the number of real solutions of $12 x^{2} - x + 3 = 0$ .

[3]

Question 12

Skill question

How many real roots does the equation $x^{2} + x + 1 = 0$ have?

[2]

Question 13

Skill question

Determine the number of real roots of $5 x^{2} - 20 x + 20 = 0$ .

[3]

IB Mathematics Analysis and Approaches Question Type 3: Finding How Many Roots the Quadratic Has Exercises