## SOLVING QUADRATIC EQUATIONS BY FACTORING WORD PROBLEMS

Solving Quadratic Equations by Factoring Word Problems :

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 equation obtained in any one of the methods

Step 3 :

Relate the mathematical solution obtained to the statement asked in the question.

## Solving Word Problems on Quadratic Equations - Examples

Example 1 :

The product of two successive multiples of 3 is 810. Find the multiples

Solution :

Let x and (x + 3) are successive multiples of 3

The product of two successive multiples  =  810

x (x + 3) = 810

x2 + 3x  =  810

x2 + 3x - 810  =  0

(x + 30) (x - 27)  =  0

 x + 30  =  0x  =  -30 x - 27  =  0x  =  27

Therefore the required multiples are 27 and 30.

Verification :

The product of two successive multiples of 3 is 810

=  27 (27 + 3)

=  27 (30)

=  810

Example 2 :

The sum of the squares of two natural numbers is 34 and sum of 5 times the smaller and 3 times the larger is 30. Find the numbers.

Solution :

Let x be the smaller natural number

and y be the larger natural number

The sum of their squares  =  34

x2 + y2  =  34

Sum of 5 times the smaller and 3 times the larger is 30

5x + 3y  =  30

5x  =  30 - 3y

x  =  (30 - 3y)/5

[(30 - 3 y)/5]2 + y2  =  34

(900 - 180y + 9y2)/25 + y2  =  34

(900 - 180y + 9y2 + 25y²)/25  =  34

34y² - 180y + 900  =  850

34y² - 180y + 900 - 850  =  0

34y2 - 180 y + 50  =  0

(34y - 10) (y - 5)  =  0

 34y - 10  =  034y  =  10y  =  10/34y  =  5/17 y - 5  =  0y  =  5

If y = 5, then x  =  [30 - 3(5)]/5

x  =  (30 - 15)/5

x  =  15/5

x  =  3

Verification :

sum of the squares of two natural numbers is 34

52 + 32  =  34

25 + 9  =  34

34  =  34

Sum of 5 times the smaller and 3 times the larger is 30

5(3) + 3(5)   = 30

15 + 15  =  30

30  =  30

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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WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

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Complementary and supplementary angles word problems

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Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

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Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6