Question

For the quadratic equation $a x^{2}+b x+c=0$ the discriminant is $D=$ ___ . The discriminant tells us how many real solutions a quadratic equation has. If $D>0,$ the equation has _ real solution (s). If $D=0,$ the equation has _ real solution (s) If $D<0,$ the equation has ___ real solution(s).

Name: Problem 3, Chapter 1: Algebra and Trigonometry
Uploaded: 2021-07-29T18:11:02-08:00
Duration: 49 s
Channel: Sari Ogami
Description: For the quadratic equation a x^2+b x+c=0 the discriminant is D= . The discriminant tells us how many real solutions a quadratic equation has. If D>0, the equation has real solution (s). If D=0, the equation has real solution (s) If D<0, the equation has real solution(s).

   For the quadratic equation $a x^{2}+b x+c=0$ the discriminant is $D=$ _____ . The discriminant tells us how many real solutions a quadratic equation has.
If $D>0,$ the equation has _____ real solution (s).
If $D=0,$ the equation has _____ real solution (s)
If $D<0,$ the equation has _____ real solution(s).

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 1, Problem 3

Instant Answer

Solved by Expert Sari Ogami

07/29/2021

Step 1

Step 1: The discriminant of a quadratic equation $ax^{2}+bx+c=0$ is given by the formula $D=b^{2}-4ac$. Show more…

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For the quadratic equation $a x^{2}+b x+c=0$ the discriminant is $D=$ _____ . The discriminant tells us how many real solutions a quadratic equation has. If $D>0,$ the equation has _____ real solution (s). If $D=0,$ the equation has _____ real solution (s) If $D<0,$ the equation has _____ real solution(s).

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants with a not equal to zero. It represents a parabolic relationship and is fundamental in algebra, allowing for the modeling of various phenomena in physics, economics, and engineering.

Discriminant

The discriminant of a quadratic equation is given by the expression b² - 4ac. This value is crucial because it determines the nature of the roots of the equation without actually solving it.

Relationship Between Discriminant and Roots

The sign of the discriminant indicates the number and type of solutions: if it is positive (>0), the equation has two distinct real solutions; if it is zero (0), there is one real solution (a repeated root); and if it is negative (<0), there are no real solutions, but the equation has two complex conjugate solutions.

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