Q. 35.0( 4 Votes )

The sum of two natural numbers is 28 and their product is 192. Find the numbers.

Answer :

Let the required number be x and 28 – x

According to given condition,


x(28 – x) = 192


x2 – 28x + 192 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = – 28 c = 192


= 1.192 = 192


And either of their sum or difference = b


= – 28


Thus the two terms are – 16 and – 12


Sum = – 16 – 12 = – 28


Product = – 16. – 12 = 192


x2 – 28x + 192 = 0


x2 – 16x – 12x + 192 = 0


x(x – 16) – 12(x – 16) = 0


(x – 16) (x – 12) = 0


(x – 16) = 0 or (x – 12) = 0


x = 16 or x = 12


Hence the required numbers are 16, 12


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Get To Know About Quadratic Formula42 mins
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic EquationsFREE Class
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Balance the Chemical Equations49 mins
Champ Quiz | Quadratic Equation48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses