Application of Quadratic Equation (Problem Solving)

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Application on Quadratic Equation

1.) The sum of a number and its reciprocal is

. What is the number?

GIVEN: Let x be thenumberbe the reciprocal of the number

QUADRATIC FORMULA

COMPLETING THE SQUARE

x =

2.) The product of two numbers is 2, and one number is 4 more than the other. Find the numbers. GIVEN: Let x be the first number

� ��



3.) Tom increased the area of his garden by 165 The rectangular garden was originally 16 ft by 12

ft, and he increased the length and the width by the same amount. Find the dimensions of the

garden now.

GIVEN: Let x be the number of feet added to each side

be the new length

be the new width

Both measurements are in feet.

Standard Formula:

Area = Length x Width

new area = original area + added area

SOLUTION:

4.) ABE Students have a project in MATH 17. They are to make a triangle sheet of canvass with a base

1 meter more than its height. The area is 0.72m2. Find the height and length of the base of the

triangle.

Given: Let x be the height be the base

Standard Formula:

Area of a triangle =

Solution:

0.72 = (x + 1)(x)

1.44 = (x + 1)(x)

1.44 = x2

+ x

X2

+ x 1.44 = 0



5.) The inclined ladder used by an ABE student in climbing a coconut is 8 meters longer than the

coconut tree. The distance between the ladder and the base of the tree is 7 meters longer than

the tree. How long are the 3 sides of the ramp?

GIVEN: Let x be the rise of the ramp (height of the triangle, a) ��

6.) A masons helper requires 4 hours more to pave a concrete walk than it takes the mason. The two

work together for 3 hours when the mason is called away. The helper completes the job in two

hours. How long does it take each to do the job working done?

Given:

Let x = the number of hours it takes the mason to do the job

X + 4 = the number of hours it takes the helper to do the job

= part of the job done by the helper in one hour

= part of the job done by the master in one hour.

Solution: Since the mason works for 3 hours and the helper works for 3 hours + 2 hours to complete

the job, therefore;

+ = 1

+

= 1

+

=

3(x + 4) + 5x= x(x + 4)3x + 12 + 5x = + 4x + 4x 5x 3x 12 = 0 4x 12 =0

(x -6)(x + 2) = 0

X = 6 and x = -2 (discarded)

c = x + 8

b= x+7

a=x

Application of Quadratic Equation (Problem Solving)

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