Question

(9) In a series of four cricket matches, the runs scored by India and Australia
are given below
Match
India
Australia
First
102
208
202
Second
192
Third
360
241
Fourth
276
203
(i) What is the average score of India in a match?
(it) What is the average score of Australia in a match?
(iii) Which team performed better?​

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.