Gr 11 Math Ch 2: Nature of Roots

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What is the nature of the roots of a quadratic equation when the discriminant is less than zero?

The roots are imaginary. (correct)

The roots are rational.

The roots are real and unequal.

The roots are real and equal.

What is the value of the discriminant when a quadratic equation has exactly one real root?

Delta is undefined.

Delta is greater than zero.

Delta is equal to zero. (correct)

Delta is less than zero.

What is the formula for calculating the discriminant of a quadratic equation?

Delta = b^2 - 4ac (correct)

Delta = b^2 + 4ac

Delta = a^2 - 4bc

Delta = a^2 + 4bc

When the discriminant is greater than zero, what can be said about the roots of the quadratic equation?

The roots are real and unequal. Signup and view all the answers

What is the condition for a quadratic equation to have rational roots?

Delta is a perfect square. Signup and view all the answers

What is the first step in calculating the discriminant of a quadratic equation?

Identify the coefficients a, b, and c. Signup and view all the answers

What is the relationship between the discriminant and the type of roots of a quadratic equation?

The discriminant determines the type of roots. Signup and view all the answers

When the discriminant is not a perfect square, what can be said about the roots of the quadratic equation?

The roots are always irrational. Signup and view all the answers

What is the nature of the roots of a quadratic equation when the discriminant is equal to zero?

Exactly one real root Signup and view all the answers

What is true about the roots of a quadratic equation when the discriminant is a perfect square?

The roots are always rational Signup and view all the answers

What is the purpose of calculating the discriminant of a quadratic equation?

To determine the type of roots the equation has Signup and view all the answers

When the discriminant is greater than zero, what can be said about the roots of the quadratic equation?

The roots are always real and unequal Signup and view all the answers

What is the relationship between the discriminant and the number of real roots of a quadratic equation?

The discriminant determines whether the roots are real or imaginary Signup and view all the answers

What is the condition for a quadratic equation to have imaginary roots?

The discriminant is less than zero Signup and view all the answers

What is the relationship between the discriminant and the type of roots of a quadratic equation?

The discriminant determines the type of roots Signup and view all the answers

What is the significance of the discriminant being greater than or equal to zero?

The equation has real roots Signup and view all the answers

What is the primary purpose of calculating the discriminant of a quadratic equation?

To determine the nature of the roots of the quadratic equation Signup and view all the answers

What is the condition for a quadratic equation to have one real root?

Δ = 0 Signup and view all the answers

What is the relationship between the discriminant and the number of real roots of a quadratic equation?

The discriminant determines the nature of the roots, not the number Signup and view all the answers

What is the condition for a quadratic equation to have two distinct real roots?

Δ > 0 Signup and view all the answers

What is the relationship between the discriminant and the type of roots of a quadratic equation?

The discriminant determines the type of roots Signup and view all the answers

What is the significance of the discriminant being a perfect square?

The roots are rational Signup and view all the answers

What is the nature of the roots of a quadratic equation when the discriminant is greater than zero?

Real and unequal Signup and view all the answers

What is the purpose of calculating the discriminant of a quadratic equation in the context of problem-solving?

To determine the nature of the roots Signup and view all the answers

What is the relationship between the discriminant and the number of roots of a quadratic equation?

If the discriminant is greater than zero, the quadratic equation has two real roots. Signup and view all the answers

What can be said about the roots of a quadratic equation when the discriminant is a perfect square?

The roots are always rational. Signup and view all the answers

What is the significance of the discriminant being equal to zero?

The quadratic equation has exactly one real root. Signup and view all the answers

What can be said about the roots of a quadratic equation when the discriminant is greater than zero?

The roots are always real and unequal. Signup and view all the answers

What is the purpose of calculating the discriminant of a quadratic equation in the context of solving quadratic equations?

To determine the type of roots of the equation. Signup and view all the answers

What can be said about the roots of a quadratic equation when the discriminant is less than zero?

The roots are always imaginary. Signup and view all the answers

What is the relationship between the discriminant and the type of roots of a quadratic equation?

The discriminant determines the type of roots. Signup and view all the answers

What can be said about the roots of a quadratic equation when the discriminant is greater than or equal to zero?

The roots are always real. Signup and view all the answers

Gr 11 Math Ch 2: Nature of Roots

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Questions and Answers

What is the nature of the roots of a quadratic equation when the discriminant is less than zero?

What is the value of the discriminant when a quadratic equation has exactly one real root?

What is the formula for calculating the discriminant of a quadratic equation?

When the discriminant is greater than zero, what can be said about the roots of the quadratic equation?

What is the condition for a quadratic equation to have rational roots?

What is the first step in calculating the discriminant of a quadratic equation?

What is the relationship between the discriminant and the type of roots of a quadratic equation?

When the discriminant is not a perfect square, what can be said about the roots of the quadratic equation?

What is the nature of the roots of a quadratic equation when the discriminant is equal to zero?

What is true about the roots of a quadratic equation when the discriminant is a perfect square?

What is the purpose of calculating the discriminant of a quadratic equation?

When the discriminant is greater than zero, what can be said about the roots of the quadratic equation?

What is the relationship between the discriminant and the number of real roots of a quadratic equation?

What is the condition for a quadratic equation to have imaginary roots?

What is the relationship between the discriminant and the type of roots of a quadratic equation?

What is the significance of the discriminant being greater than or equal to zero?

What is the primary purpose of calculating the discriminant of a quadratic equation?

What is the condition for a quadratic equation to have one real root?

What is the relationship between the discriminant and the number of real roots of a quadratic equation?

What is the condition for a quadratic equation to have two distinct real roots?

What is the relationship between the discriminant and the type of roots of a quadratic equation?

What is the significance of the discriminant being a perfect square?

What is the nature of the roots of a quadratic equation when the discriminant is greater than zero?

What is the purpose of calculating the discriminant of a quadratic equation in the context of problem-solving?

What is the relationship between the discriminant and the number of roots of a quadratic equation?

What can be said about the roots of a quadratic equation when the discriminant is a perfect square?

What is the significance of the discriminant being equal to zero?

What can be said about the roots of a quadratic equation when the discriminant is greater than zero?

What is the purpose of calculating the discriminant of a quadratic equation in the context of solving quadratic equations?

What can be said about the roots of a quadratic equation when the discriminant is less than zero?

What is the relationship between the discriminant and the type of roots of a quadratic equation?

What can be said about the roots of a quadratic equation when the discriminant is greater than or equal to zero?

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