Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
The Square Root Property
4:30 minutes
Problem 89a
Textbook Question
Textbook QuestionEvaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. 9x^2 + 11x + 4 = 0
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Discriminant
The discriminant is a key component of a quadratic equation in the form ax^2 + bx + c = 0, represented by the formula D = b^2 - 4ac. It helps determine the nature of the roots of the equation. If D > 0, there are two distinct real solutions; if D = 0, there is exactly one real solution; and if D < 0, the solutions are nonreal complex numbers.
Recommended video:
04:11
The Discriminant
Nature of Solutions
The nature of solutions refers to the characteristics of the roots of a quadratic equation based on the value of the discriminant. Distinct solutions can be rational (if they can be expressed as a fraction of integers), irrational (if they cannot be expressed as such but are still real), or nonreal complex (if the solutions involve imaginary numbers). Understanding this helps in predicting the behavior of the quadratic function.
Recommended video:
2:51
The Natural Log
Quadratic Equations
Quadratic equations are polynomial equations of degree two, typically expressed in the standard form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. They can be solved using various methods, including factoring, completing the square, or applying the quadratic formula. The study of their solutions and properties is fundamental in algebra and has applications in various fields.
Recommended video:
05:35
Introduction to Quadratic Equations
Watch next
Master Solving Quadratic Equations by the Square Root Property with a bite sized video explanation from Callie
Start learning