Question

b) The organisers of a dance competition decided that the winners of the competition would
get a prize money of 5000 each and the participants who did not win would get 750
each. The total prize money distributed was 1,60,000
(1) Find the number of winners, if the total number of participants was 100
() Out of the total number of winners, the number of girls was three times the number of
boys. Find the number of boys and the number of girls who won.​

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.

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