Statement sum Involing Quadratic Equations


 
 
Concept Explanation
 

Statement sum Involing Quadratic Equations

Statement sum Involving  Quadratic Equations:

Step 1: Translate the word problem into methamatical statement.

Step 2:  Then form a Quadratic Equation.

Step 3: Solve the Quadratic Equation.

Step 4: Reject the root that satisfy the conditions of the problem.

Example: The Sum of two numbers is 18 and their product is 45. Find the numbers.

Solution: Let one number = y

 Other number = 18- y

According to the question:

Product = 45

y X (18-y) = 45

large 18y-y^2=45

large -y^2+18y-45=0

large y^2-18y +45=0

large y^2-15y -3y+45=0

large y(y-15) -3(y-15)=0

large (y-15) (y-3)=0

large Either ;(y-15) =0 ;or; (y-3)=0

y= 15 , 3

So One number is 15 and the other number is 3

Sample Questions
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Question : 1

A number is multiplied by    large frac{1}{3}    times itself and 18 is added to the result. If the final result is 2901, the number is _________________

Right Option : B
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Question : 2

One side of a rectangle is 3 ft shorter than twice the other side. Find the sides if the perimeter is 24 ft.

Right Option : A
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Question : 3

A businessman knows that the price of a commodity will increase by Rs. 5 per packet. He buys some packets of the commodity for Rs. 4500. If he buys them on new price, then he will get 10 packets less. Find the actual number of packets bought by him.

Right Option : C
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