Pull down options: zero, one, two ### Determining the Number of Real Solutions of a Quadratic Equation Using the DiscriminantFor the quadratic equation \( ax^2 + bx + c = 0 \), the discriminant is \( D = \). The discriminant tells us how many real solutions a quadratic equation has.- If \( D > 0 \), the equation has \( \text{Select} \) real solution(s).- If \( D = 0 \), the equation has \( \text{Select} \) real solution(s).- If \( D < 0 \), the equation has \( \text{Select} \) real solution(s). ### ExplanationThe discriminant of a quadratic equation \( ax^2 + bx + c \) is found using the formula:\[ D = b^2 - 4ac \]The value of \( D \) determines the nature and number of the solutions:- **When \( D > 0 \)**: There are two distinct real solutions.- **When \( D = 0 \)**: There is exactly one real solution (a repeated or double root).- **When \( D < 0 \)**: There are no real solutions; instead, there are two complex conjugate solutions.### Practical ApplicationTo use the discriminant effectively, identify the coefficients \( a \), \( b \), and \( c \) from the quadratic equation \( ax^2 + bx + c = 0 \). Substitute these values into the discriminant formula \( D = b^2 - 4ac \) and evaluate \( D \). Based on the value of \( D \):- Use the criteria outlined above to determine the number of real solutions.- For example, if the discriminant \( D \) is positive, you can conclude that there are two real solutions.This method provides a quick way to understand the nature of the roots of the quadratic equation without solving it completely.

Quadratic equation ax2+bx+c=0 D= b2 -4ac

For the quadratic equation ax + bx +c = 0, the discriminant is D = The discriminant tells us how many real solutions a quadratic equation has. If D> 0, the equation has -Select- If D = 0, the equation has If D< 0, the equation has v real solution(s). Select--- V real solution(s). Select-V real solution(s).

For the quadratic equation ax + bx +c = 0, the discriminant is D = The discriminant tells us how many real solutions a quadratic equation has. If D> 0, the equation has -Select- If D = 0, the equation has If D< 0, the equation has v real solution(s). Select--- V real solution(s). Select-V real solution(s).

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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