(a.)
To Explain: A quadratic function or equation in standard form can be written if the roots are known.
It has been explained how a quadratic function or equation in standard form can be written if the roots are known.
Given:
The roots of a
Concept used:
There is a relation between the roots of a quadratic equation and its coefficients.
Calculation:
Let the roots of a quadratic equation be
Then, the quadratic equation can be written as
Simplifying,
On further simplification,
Finally,
So, the quadratic equation, whose roots are
Conclusion:
It has been explained how a quadratic function or equation in standard form can be written if the roots are known.
(b.)
To Demonstrate: The method for writing the quadratic equation in standard form for each pair of roots given.
The method for writing the quadratic equation in standard form for each pair of roots given has been demonstrated.
Given:
The following pairs of roots:
Concept used:
There is a relation between the roots of a quadratic equation and its coefficients.
Calculation:
As determined previously, the quadratic equation, whose roots are
The first pair of roots is
So,
Put these values in
Simplifying,
This is the required quadratic equation.
The second pair of roots is
So,
Put these values in
Simplifying,
On further simplification,
Finally,
This is the required quadratic equation.
The third pair of roots is
So,
Put these values in
Simplifying,
This is the required quadratic equation.
The fourth pair of roots is
So,
Put these values in
Simplifying,
This is the required quadratic equation.
The fifth pair of roots is
So,
Put these values in
Simplifying,
On further simplification,
Finally,
This is the required quadratic equation.
Conclusion:
The method for writing the quadratic equation in standard form for each pair of roots given has been demonstrated.
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education