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Chapter 0: Problem 155

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

Short Answer

Expert verified
The discriminant in a quadratic equation is the expression under the square root in the quadratic formula (鈭� = B虏 - 4AC). It provides information about the roots of a quadratic equation. If 鈭� is positive, there are two distinct real roots, if it equals to zero, there's one real (repeated) root and if it's negative, there are two complex roots.

Step by step solution

01

Discriminant Definition

The discriminant refers to the term \( \Delta = B^2 - 4AC \) under the square root in the quadratic formula used to find the solutions of a quadratic equation in the form of \( Ax^2 + Bx + C = 0 \), where A, B and C are constants and A 鈮� 0.
02

The Significance of the Discriminant Value

The value of the discriminant (螖) gives information about the roots of a quadratic equation. If 螖 > 0, the equation has two distinct real roots. If 螖 = 0, the equation has one real root (or a repeated root.) If 螖 < 0, the equation has two complex roots.
03

Example

Consider the quadratic equation \( x^2 - 5x + 6 = 0 \). Here, A = 1, B = -5, and C = 6. We calculate the discriminant as: \( \Delta = B^2 - 4AC = (-5)^2 - 4*1*6 = 25 - 24 = 1 \) which is greater than zero. Hence, the given quadratic equation has two distinct real roots.

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