Factorization Of Quadratic Equations II – – Word Problems SS1 Mathematics Lesson Note

WORD PROBLEM LEADING TO QUADRATIC EQUATIONS

Examples

1. Find two numbers whose difference is 5 and whose product is 266.

Solution

Let the smaller number be x.

Then the smaller number is x+5.

Their product is x(x+5) .

Hence, 

x(x+5) = 266

x2+5x-  266 = 0

(x-14)(x+19)=0

 x=14 or x= -19

The other number is 14+5 or  -19+5 i.e 19 or -14 

:. The two numbers are 14 and 19 or -14 and -14.

2. Tina is 3 times older than her daughter. In four years, the product of their ages will be 1536. How old are they now?

Solution

Let the daughter’s age be x.

Tina’s age = 3x

In four years,

Daughter’s age = (x+4)years

Tina’s age = (3x+4)years

The product of their ages :

 (x+4)(3x+4)= 1536

3×2+ 16x – 1520 = 0

(x-20)(3x+76) = =0

 x=20 or x=-25.3

Since age cannot be negative, x=20 years.

:. Daughter’s age = 20 years.

 Tina’s age = 20×3=60 years.   

ASSIGNMENT 

1. The area of a rectangle is 60 cm2. The length is 11cm more than the width. Find the width.
2. A man is 37 years old and his child is 8. How many years ago was the product of their age 96?
3. If α and β are the roots of the equation 2×2 – 9x+4=0, find a) α + β      (b) αβ       (c) α – β   (d)  αβ/ α + β