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Chapter 1: Problem 160

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

Short Answer

Expert verified
The discriminant is a component of the quadratic formula that determines the nature of the roots of the equation. Specifically, if the discriminant is greater than 0, the equation has two distinct real roots; if it's equal to 0, the equation has two equal real roots (or one real root); and if it's less than 0, the equation has no real roots but two complex roots.

Step by step solution

01

Find the discriminant

Substitute the values of 'a', 'b', and 'c' from the quadratic equation into the formula for the discriminant: \( b^2 - 4ac \). The result obtained is called the discriminant and denoted as 'D'. If the equation is \( ax^2 + bx + c = 0 \), then \( D = b^2 - 4ac \).
02

Determine the nature of roots

Use the value of 'D' to determine the nature of the roots of the quadratic equation:1. If \( D > 0 \), the equation has two distinct real roots.2. If \( D = 0 \), the equation has two equal real roots (or one real root).3. If \( D < 0 \), the equation has no real roots. Instead, the equation has two complex roots.

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