
UNIT 3 : QUADRATIC FUNCTIONS & EQUATIONS
LESSON
4: PROBLEM SOLVING WITH QUADRATIC
EQUATIONS
Quadratic Equation Problems
Number
Problems:
Example 1:
Two
integers differ by 4. The sum of their
squares is 250. Find the integers.
Solution:
à Determine
what is unknown or what you are asked to find?
Assign variables to the unknowns.
Here we are asked to find two numbers. Let the first number be x and the second
number be y.
à We are told the sum of their squares is 250. Write this statement as an equation.
à Write this as an equation in one
variable.
Since
the integers differ by 4, we have a secondary relation between the two
variables, namely,
Check (i)
The integers differ by 4.
(9)(13) = 4 and
13 – 9 = 4
Check(ii)
The sum of their squares is 250.
(9)^{2} + (13)^{2}
= 81 + 169 = 250 and
9^{2} + 13^{2} = 81 + 169 = 250
Example 2:
The sum
of two numbers is 25 and their product is 156.
Find the numbers.
Solution:
à Determine
what is unknown or what you are asked to find?
Assign variables to the unknowns.
Here we
are asked to find two numbers. Let
the first number be x and the second number be y.
à We are told their product is 156. Write this statement as an equation.
à Write this as an equation in one
variable.
Since
their sum is 25, we have a secondary relation between the two variables,
namely,
Check (i)
Their sum is 25
12
+ 13 = 25
Check (ii)
Their product is 156
(12)(13) = 156
Area
Problems:
x + 7
x
x
(60+2x)
(80
+ 2x)
x
y
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Quadratic Equation Problems homework questions 