Quadratic Formula Discriminant Quiz

Questions and Answers

What is the formula for the discriminant?

b^2 - 4ac

If the value of the discriminant is positive (d > 0) and it is a perfect square, how many roots does the quadratic equation have?

Two real, rational roots (correct)

No real roots

Two complex roots

One real, irrational root

If the value of the discriminant is positive (d > 0) but it is not a perfect square, what can be said about the roots?

Two real, rational roots

Two real, irrational roots (correct)

No real roots

One real, rational root

What is the result if the value of the discriminant is zero (d = 0)?

<p>One real, rational root</p> Signup and view all the answers

If the value of the discriminant is negative (d < 0), what does it imply about the roots?

<p>Two complex roots</p> Signup and view all the answers

Study Notes

Quadratic Formula Discriminant

The discriminant formula is expressed as b² - 4ac. It determines the nature of the roots in a quadratic equation.

Discriminant Outcomes

A positive discriminant (d > 0) that is a perfect square results in two real, rational roots. This indicates that the roots can be expressed as fractions and are rational numbers.
A positive discriminant (d > 0) that is not a perfect square leads to two real, irrational roots. This means the roots cannot be expressed as simple fractions, resulting in non-repeating, non-terminating decimals.
When the discriminant is zero (d = 0), it indicates there is one real, rational root. In this case, the quadratic touches the x-axis at exactly one point, known as a double root.
A negative discriminant (d < 0) implies that there are no real roots, only complex roots. The quadratic does not intersect the x-axis.

Understanding the Quadratic Formula

The quadratic formula used to find roots is: x = (-b ± √(b² - 4ac)) / 2a. This formula utilizes the discriminant to determine the nature of the roots.

Description

Test your understanding of the discriminant in quadratic equations. This quiz covers the various outcomes based on the value of the discriminant, including rational and irrational roots, as well as the conditions for real and complex roots. Dive into the details of how discriminants influence the nature of roots!