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

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

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

Question 1

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

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Question 2

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

[3]

Question 3

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

[3]

Question 4

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

[3]

Question 5

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

[4]

Question 6

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

[3]

Question 7

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

[3]

Question 8

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

[3]

Question 9

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

[4]

Question 10

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

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

[3]

Question 11

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

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

[4]

Question 12

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.

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