Q. 28

The sum of a number and its reciprocal is . The number is
A.

B.

C.

D.

Answer :

Let the required number be x


According to the question




20x2 - 41x + 20 = 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 = 20 b = - 41 c = 20


= 20.20 = 400


And either of their sum or difference = b


= - 41


Thus the two terms are - 25 and - 16


Difference = - 25 - 16 = - 41


Product = - 25. - 16 = 400


20x2 - 25x - 16x + 20 = 0


5x(4x - 5) - 4(4x - 5) = 0


(5x - 4) (4x - 5) = 0


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