Question

In a survey of a community, 55% of the people like to listen to the radio,
65% like to watch television and 35% like to listen the radio as well as watch
television.
(i)
Show the above information in a Venn-diagram.
(ii) Find the percentage of the people who do not like to listen to radio as well
as watch television.
120 lilood football 90 liked​

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.