Question

In a survey of a community, 55% of the people like to listen the radio70% like to watch the
television and 35% like to listen radio as well as to watch television.find the percentage of
people who did not like to listen radio as well as to watch the television.
a 10%
b. 20%
c.35%
d.40
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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.