Activity 1: I Can Fill It! Below Is A Problem Where You Can Solve By Simply Following Th…
Activity 1: I Can Fill it!
Below is a problem where you can solve by simply following the steps that can be found
at the right side. Fill in the blank spaces with the needed solution. In each activity, write
your answers on a separate sheet of paper
Problem: The sum of the square of a number and 15 is the same as eight times the
number. What are the numbers?
What To Do
Solution
Use a variable to represent the
unknown
Let I be the number
=
+ 15
Translate into mathematical
expression
Place polynomial on one side and
set equation to zero by Additive
Inverse Property
r? + 15
=Bx
Write the resulting equation
x2 + 15 – 8x
Arrange the terms in descending
order of its exponents
x2 – 8x +
Factor the polynomial
= 0
()()
(x – 2) = 0 or (x – 2) = 0 Apply the Zero Property
x-5 + – = 0+ – or
Solve for the unknown by using
Additive Inverse Property
*_ + 3 = 0 +-
Write the resulting equation.
1 =
or
–
X =
Final Statement: The numbers are
FINDING THE ROOTS OF A QUADRATIC EQUATION
Problem:
The sum of the square of a number and 15 is the same as eight times the
number. What are the numbers?
What To Do
Solution:
Step 1: Use a variable to represent the unknown.
Let x be the number. Translate into a mathematical equation.
[tex]x^{2}+15=8x[/tex]
Step 2: Place polynomial on one side and set equation to zero by Additive Inverse Property
[tex]x^{2}+15 – 8x =8x-8x\\[/tex]
Write the resulting equation
[tex]x^{2}+15-8x=0[/tex]
Step 3: Arrange the terms in descending order of its exponents.
[tex]x^{2} -8x+15=0[/tex]
Step 4: Factor the polynomial. Apply the Zero Property.
[tex](x-3)(x-5)=0[/tex]
Step 5: Solve for the unknown by using Additive Inverse Property.
For x-3=0:
[tex]x-3 =0\\x-3+3=+3\\x=3[/tex]
For x-5=0:
[tex]x-5 =0\\x-5+5=+5\\x=5[/tex]
Step 6: Write the resulting equation.
[tex]x=3 \\and\\x=5[/tex]
Final Statement: The numbers are 3 and 5.
REMEMBER: Since the degree of a quadratic equation is 2, this implies that the maximum number of roots it has is 2. However, not both roots of a quadratic equation satisfies it. This root is called an extraneous root.
Read more about quadratic equation:
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