Question

c) In 2009, the rise in the number of Metro train travelers reduced the consumption of
CNG, diesel and petrol. It is estimated that 33000 tonnes of CNG, 3300 tonnes of
diesel, and 21000 tonnes of petrol had been saved in 2009. Find the ratio of
(i) the quantity of diesel saved to the quantity of petrol saved.
(ii) the quantity of diesel saved to the quantity of CNG saved.​

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.