Question

Underground water sump is constructed to store large amount
of water. A builder wants to build a cuboidal sump for a flat to
store 20m3 of water.

i. What should be the depth of the sump if the length and
breadth of sump are 2m each.
ii. Find the capacity of the sump in litres.
iii. If the residents in the flat need 5000 litres per day, how long
will the water in the sump last?
iv. If one person needs 100 litre per day, how many persons are
there in the flat?

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.