PPT-lesson14CollegeAdvanceAlgebra2023.pdf

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UDM PRAYER
Almighty GOD, creator and giver of life
We give You thanks and vow to seek Your light
Through the knowledge that we gain and impart with our peers
In our dear University
Grant us forgiveness for the sins we confess
And give us strength to discern what is best
For ourselves, and more so,
For the benefit of others
Teach us to have grateful hearts and enlightened minds
As we learn and share our talents to the community
For the greater good and a brighter future
Of the City of Manila and our country
All these for Your greater glory.
AMEN.

2. LESSON #14: Relationship between Roots
and Coefficient
UNIVERSIDAD DE MANILA
COLLEGE OF EDUCATION
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CHAPTER V: QUADRATIC EQUATION

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Learning Objectives
1] determine the relationship between roots and coefficient;
2] demonstrate mathematical skills in finding the sum and product
of the roots;
3] find a quadratic equation with integral coefficients whose roots
are the given number and;
4] apply the method/s in solving quadratic equation with
self-confidence and accuracy.
At the end of the discussion, learners should be able to:

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SUM AND PRODUCT OF THE ROOTS
If �,� are the roots of ax
2
+ bx + c = 0, then
?????? ��� �� �����= �+ � = −
�
�
???????????? ������� �� �����= � � =
�
�
?????????????????? �ℎ� �����??????�� ??????� ���??????������ ���− ��−�=0
�
2
−�+��+ ��=0

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A] Find the sum and product of the
roots.

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1] �
2
+6�+5=0
SOLUTION AND ANSWER:
Sum of roots =
−6
1
= −�
Product of roots =
5
1
=�

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3] 2�
2
−�−7=0
SOLUTION AND ANSWER:
Sum of roots =
−(−1)
2
=
�
�
Product of roots =
−�
�

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5] 4�
2
−12�+9=0
SOLUTION AND ANSWER:
Sum of roots =
−(−12)
4
= �
Product of roots =
�
�

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7] 7�
2
−4=0
SOLUTION AND ANSWER:
Sum of roots =
0
7
= �
Product of roots =
−�
�

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9] 3�
2
−4�+2=0
SOLUTION AND ANSWER:
Sum of roots =
−(−4)
3
=
�
�
Product of roots =
�
�

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PRACTICE EXERCISES

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A] Find the sum and product of the
roots.

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2] �
2
+2�+6=0
4] 2�
2
+5�+5=0
6] 3�
2
+7�−1=0
8] 5�
2
+3=0
10] �
2
+5� -2=0

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B] Find a quadratic equation with
integral coefficients whose roots
are the given number.

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1] 2,−1
SOLUTION AND ANSWER:
�ℎ� �����??????���− ��−�=0
??????� ���??????������ �� �
2
−�+��+ ��=0
Sum: 2+−1=1
Product: 2−1=−2
??????
�
−??????−�=�

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3]
2
3
,−
4
3
SOLUTION AND ANSWER:
�ℎ� �����??????���− ��−�=0
??????� ���??????������ �� �
2
−�+��+ ��=0
Sum:
2
3
+−
4
3
= −
2
3
Product:
2
3
−
4
3
=−
8
9
??????
�
+
�
�
??????−
�
�
=�
�??????
�
+�??????−�=�

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5] 2??????,−2??????
SOLUTION AND ANSWER:
�ℎ� �����??????���− ��−�=0
??????� ���??????������ �� �
2
−�+��+ ��=0
Sum: 2??????+(−2??????)=�
Product: 2??????−2??????=−4??????
2
=−4−1=�
??????
�
+�=�

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7] 3−??????,3+??????
SOLUTION AND ANSWER:
�ℎ� �����??????���− ��−�=0
??????� ���??????������ �� �
2
−�+��+ ��=0
Sum: 3−??????+3+??????=�
Product: 3−??????3+??????=9−??????
2
=9−−1=��
??????
�
−�??????+��=�

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9] 3 ±??????7
SOLUTION AND ANSWER:
�ℎ� �����??????���− ��−�=0
??????� ���??????������ �� �
2
−�+��+ ��=0
Sum: 3+??????7+3−??????7=��
Product: 3+??????73−??????7=3−??????
2
49=3−−17=3+7=��
??????
�
−��??????+��=�

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PRACTICE EXERCISES

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B] Find a quadratic equation with
integral coefficients whose roots
are the given number.

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2] 3,4
4] −
3
2
,
4
5
6] 2,−2
8] 3 ±3
10] 2 ±5

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Thank You!!!
LAUS DEO SEMPER
Prepared by:
Willie C. Delmo
CED, Faculty

26. Any Questions
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REFERENCES/TEXTBOOK/LINKS
Louis Leithold, College Algebra and Trigonometry, Addison-
Wesley Publishing Company, 1992 Mandaluyong City:
National Book Store, Inc., 1992).
College Algebra by Prentice Hall
College Algebra (4
th
Edition) by Gordon Fuller
MSA Advanced Algebra by Merle S. Alferez

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