Gr 11 Math Ch 2: Nature of Roots
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Gr 11 Math Ch 2: Nature of Roots

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@GreatestTiger

Questions and Answers

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

The roots are imaginary.

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

Delta is equal to zero.

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

Delta = b^2 - 4ac

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

<p>The roots are real and unequal.</p> Signup and view all the answers

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

<p>Delta is a perfect square.</p> Signup and view all the answers

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

<p>Identify the coefficients a, b, and c.</p> Signup and view all the answers

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

<p>The discriminant determines the type of roots.</p> 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?

<p>The roots are always irrational.</p> Signup and view all the answers

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

<p>Exactly one real root</p> Signup and view all the answers

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

<p>The roots are always rational</p> Signup and view all the answers

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

<p>To determine the type of roots the equation has</p> Signup and view all the answers

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

<p>The roots are always real and unequal</p> Signup and view all the answers

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

<p>The discriminant determines whether the roots are real or imaginary</p> Signup and view all the answers

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

<p>The discriminant is less than zero</p> Signup and view all the answers

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

<p>The discriminant determines the type of roots</p> Signup and view all the answers

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

<p>The equation has real roots</p> Signup and view all the answers

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

<p>To determine the nature of the roots of the quadratic equation</p> Signup and view all the answers

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

<p>Δ = 0</p> Signup and view all the answers

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

<p>The discriminant determines the nature of the roots, not the number</p> Signup and view all the answers

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

<p>Δ &gt; 0</p> Signup and view all the answers

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

<p>The discriminant determines the type of roots</p> Signup and view all the answers

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

<p>The roots are rational</p> Signup and view all the answers

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

<p>Real and unequal</p> Signup and view all the answers

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

<p>To determine the nature of the roots</p> Signup and view all the answers

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

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

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

<p>The roots are always rational.</p> Signup and view all the answers

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

<p>The quadratic equation has exactly one real root.</p> Signup and view all the answers

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

<p>The roots are always real and unequal.</p> 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?

<p>To determine the type of roots of the equation.</p> Signup and view all the answers

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

<p>The roots are always imaginary.</p> Signup and view all the answers

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

<p>The discriminant determines the type of roots.</p> 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?

<p>The roots are always real.</p> Signup and view all the answers

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