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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

92 + 132 = 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