MATHEMATICS 9 5TH MODULE NAME: Meloupe Grace M. Alburo THE DISCRIMINANT Exploring Math You have derived the quadratic formula in the proceeding lesson. Can you now solve each equation in the table? Record the value of b- 4ac and the value or values of the roots. Can you describe the nature of the solutions as shown below. Equation b-4ac Roots Description two real and unequal 3x² + 4x+1=0 4 x=13 x-1 roots ✓ 2x² + 9x + 11 = 0 2x² - 6x +9=0 -2x² + 8x + 24 = 0 -2x² + 6x-10=0 + 4x + 9-0 5x² + 2x-10-0 When the solutions to a quadratic equation are not real numbers, do they show any special relationship to each other? Describe any pattern that you find in your table. How can you use the value of b²-4ac to describe the nature of the roots of a quadratic equation? You can determine the nature of the roots without actually solving the equation. Let x, and x, denote the roots of ar²+bx+c = 0, where a, b and c are real numbers, and a # 0. Using the quadratic formula, you come up with X₁ -b+√b²-4ac 2a and X₂ -b-√b²-4ac 2a The number represented by b² - 4ac, under the radical sign is called the discriminant of the quadratic equation. The nature of the roots can be determined by finding the value of the discriminant. Consider the following examples:
MATHEMATICS 9 5TH MODULE NAME: Meloupe Grace M. Alburo THE DISCRIMINANT Exploring Math You have derived the quadratic formula in the proceeding lesson. Can you now solve each equation in the table? Record the value of b- 4ac and the value or values of the roots. Can you describe the nature of the solutions as shown below. Equation b-4ac Roots Description two real and unequal 3x² + 4x+1=0 4 x=13 x-1 roots ✓ 2x² + 9x + 11 = 0 2x² - 6x +9=0 -2x² + 8x + 24 = 0 -2x² + 6x-10=0 + 4x + 9-0 5x² + 2x-10-0 When the solutions to a quadratic equation are not real numbers, do they show any special relationship to each other? Describe any pattern that you find in your table. How can you use the value of b²-4ac to describe the nature of the roots of a quadratic equation? You can determine the nature of the roots without actually solving the equation. Let x, and x, denote the roots of ar²+bx+c = 0, where a, b and c are real numbers, and a # 0. Using the quadratic formula, you come up with X₁ -b+√b²-4ac 2a and X₂ -b-√b²-4ac 2a The number represented by b² - 4ac, under the radical sign is called the discriminant of the quadratic equation. The nature of the roots can be determined by finding the value of the discriminant. Consider the following examples:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please help
Transcribed Image Text:MATHEMATICS 9
STH MODULE
NAME: Meloure Grace M. Alburo
THE DISCRIMINANT
Explering Math
You have derived the quadratic formula in the proceeding lesson. Can you
now solve each equation in the table? Record the value of b - dac and the value
or values of the roots. Can you describe the nature of the solutions as shown
below.
Equation
- 4ac
Roots
Description
two realand unequa
roots
3x + 4x +1-0
x - 1
2x + 9x +11 -0
2x- 6x + 9 =0
-2x+ &x +24 = 0
-2x + áx -10 = 0
*+ 4x + 9-0
Sx + 2x -10 - 0
When the solutions to a quadratic equation are not real numbers, do they
show any special relationship to each other?
Describe any pattern that you find in your table. How can you use the
value of b- 4ac to describe the nature of the roots of a quadratic equation?
You can determine the nature of the roots without actually solving the
equation. Let x, and x, denote the roots of
ar + bx +c= 0, where a, b and c are real numbers, and a 0.
Using the quadratic formula, you come up with
-b + V - 4ac
X, =
and x2
-b - Nb - 4ac
2a
2a
The number represented by b - 4ac, under the radical sign is called
the discriminant of the quadratic equation. The nature of the roots can be
determined by finding the value of the discriminant.
Consider the following examples:
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
