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Chapter 11: Problem 93

What is the discriminant and what information does it provide about a quadratic equation?

Short Answer

Expert verified
The discriminant of a quadratic equation is calculated as \(b^2 - 4ac\) and provides information about the nature of the roots of the equation. If greater than 0, there are two distinct real roots. If equal to 0, one real root exists. If less than 0, two complex roots exist.

Step by step solution

01

Identify the Coefficients

The first step is to establish the a, b, and c parts from the quadratic equation. These represent coefficients within the equation that is in standard form - \(ax^2 + bx + c = 0\).
02

Calculate the Discriminant

Use the established coefficients to calculate the discriminant using the formula \(b^2 - 4ac\).
03

Interpret the Discriminant

Finally, interpret the value of the discriminant. If the discriminant is positive, there are two distinct real roots. If it equals zero, then there is one real root. If it is negative, then there are two complex roots.

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