Quadratic Function Word Problems with Answers :
In this section, we will solve some examples expressed in words and some problems describing day to day life situation involving quadratic equation.
To solve a given word problem involving quadratic equations, we follow the steps given below.
Step 1 :
Convert the word problem to a quadratic equation form.
Step 2 :
Solve the quadratic functions obtained using any one of the methods
Step 3 :
Relate the mathematical solution obtained to the statement asked in the question.
Example 1 :
Two natural numbers differ by 2 and their product is 360. Find the numbers.
Let x and y be two natural numbers
it differs by 2
x - y = 2 ----- (1)
Their product is 360
xy = 360
y = 360/x ----- (2)
Now we may apply the value of y in the first equation.
x - (360/ x) = 2
(x2 - 360)/x = 2
x2 - 360 = 2x
x2 - 2x - 360 = 0
(x + 18) (x - 20) = 0
x + 18 = 0
x = -18
x - 20 = 0
x = 20
Since it is a positive integer, we should not take x = -18. We take positive value for x.
If x = 20,
y = 360/20
y = 18
Therefore the required positive integers are 20 and 18.
Two natural numbers differ by 2.
20 - 18 = 2
their product is 360
20 (18) = 360
Example 2 :
There are three consecutive positive integers such that the sum of the square of first and the product of the other two is 154. Find the integers.
Let x, (x + 1) and (x + 2) be the first three consecutive integers
The sum of the squares of first and the product of the other two is 154
x2 + (x + 1) (x + 2) = 154
x2 + x2 + 2x + 1x + 2 = 154
2x2 + 3x + 2 = 154
2x2 + 3x + 2 - 154 = 0
2x2 + 3x - 152 = 0
(2x + 19) (x - 8) = 0
2x + 19 = 0
x = -19/2
x - 8 = 0
x = 8
Since it is positive integer, the value of x be 8.
Therefore three consecutive integers are 8, 9 and 10.
The sum of the square of first and the product of the other two is 154.
82 + (9) (10) = 154
64 + 90 = 154
154 = 154
After having gone through the stuff given above, we hope that the students would have understood how to solve word problems using quadratic equations.
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