Exercises for Question Type 7: Determining the number of real roots for a given real quadratic

Exercises for Question Type 7: Determining the number of real roots for a given real quadratic - IB

Written by official IB examiners

Question 1

Skill question

Determine the value(s) of $k$ such that the quadratic $3 x^{2} + k x + 1 = 0$ has exactly one real root.

[3]

Question 2

Skill question

Determine the number of real roots of $x^{2} + 4 x + 3 = 0$ .

[3]

Question 3

Skill question

For what values of $k$ does $x^{2} - 6 x + k = 0$ have no real roots?

[3]

Question 4

Skill question

Determine the number of real roots of the quadratic $x^{2} + x + 1 = 0$ .

[3]

Question 5

Skill question

Find the range of $k$ for which $4 x^{2} - 6 x + k = 0$ has two distinct real roots.

[4]

Question 6

Skill question

Determine the number of real roots of $5 x^{2} - 20 x + 15 = 0$ .

[3]

Question 7

Skill question

Show that the quadratic $4 x^{2} - 6 x + 5 = 0$ has no real solutions.

[3]

Question 8

Skill question

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

[3]

Question 9

Skill question

Find all real values of $k$ for which the equation $x^{2} - 2 x + k = 0$ has real roots.

[4]

Question 10

Skill question

Determine the number of real solutions for a quadratic equation using the discriminant.

Determine the number of real solutions to the quadratic equation $2 x^{2} - 5 x + 2 = 0$ .

[3]

Question 11

Skill question

Determine the number of real roots of a quadratic equation $k x^{2} + 4 x + 1 = 0$ for $k > 0$ using the discriminant.

For $k > 0$ , determine the number of real roots of $k x^{2} + 4 x + 1 = 0$ in terms of $k$ .

[4]

Question 12

Skill question

This question tests the ability to determine the range of values for a parameter such that a quadratic equation has real roots using the discriminant.

Determine all real $k$ such that the equation $x^{2} + 2 (k - 1) x + k = 0$ has real roots.

[5]

IB Mathematics Applications & Interpretation Question Type 7: Determining the Number of Real Roots for a Given Real Quadratic Exercises