Quadratic Equations

​APPLICATION OF QUADRATIC EQUATION

​Brain Break

​https://www.youtube.com/watch?v=FOgcrNrtfpo

​Objective

Solve problems involving quadratic equations

Example 1.

​The sum of two numbers is 19. The sum of the squares of the numbers is 193. Find the two numbers.

Solution:

​

Let x = one of the numbers

19 - x = the other number

x² + (19 - x)² = sum of the squares of the two numbers​

​The sum of two numbers is 19. The sum of the squares of the numbers is 193. Find the two numbers.

Solution:

​

x² + (19 - x)² = 193 sum of the squares of the numbers is 193​

x² + 361 - 38x + x² = 193 square the binomial

2x² - 38x + 168 = 0​ combine like terms

x² - 19x + 84 = 0​ divide by 2

(x - 7)(x - 12) = 0​ factor

​

x - 7 = 0 or x - 12 = 0​

x = 7 or x = 12​

Example 2.

​A square field with an enclosed area of 64 m² is to be fenced with wires. What is the dimension of the field.

Solution:

​

Let s = the length of the side of the field and A be the area

​

A square field with an enclosed area of 64 m² is to be fenced with wires. What is the dimension of the field?

Example 3.

​The area of a rectangle is 40 cm². If the length is 3 cm longer than the width, find the dimension of the rectangle.

Solution:

​

Let A = the area of the rectangle

w = width of the rectangle​​

l = w + 3 = length of the rectangle

​

​

The area of a rectangle is 40 cm². If the length is 3 cm longer than the width, find the dimension of the rectangle.

Solution:

​

A = lw

A = (w + 3)w

40 = w² + 3w

w² + 3w - 40 = 0

(w + 8)(w - 5) = 0​

​

w + 8 = 0​

w = -8​

​

w - 5 = 0​

w = 5​

​

w + 8 = 0​

w = -8​

​

Thus, the width is 5 cm and the length is w + 3 = 5 + 3 = 8 cm.

Multiple Choice

Solve.

If the product of two consecutive positive integers is 240 , what is the sum of these integers ?

• 15

• 16

• -15

• -16

• 31

​Worktext reference:

Oronce O.A., Mendoza M.O. (2019). E-Math Worktext in Mathematics 9, Manila, Philippines: REX Bookstore Inc.

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References:

Nivera G.C., Lapinid M.R.C. (2018). Grade 9 Mathematics Patterns and Practicalities 9, Makati City, Philippines: Salesiana Books by Don Bosco Press, Inc.

​

Dacanay, C.C., Demegillo, S.S. (2017). Empowering Through Math 9, Quezon City, Philippines: Ephesians Publishing Inc.​

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