9. The following scores were obtained by a group of 40 students
on an achievement test:
32 78 27 65 88 83 63 52
86 70 42 66 56 44 63 59
73 52 43 69 59 46 71
71 65
42 55 39 70 57 49 78 70
34 61 62 77 81 72 79 69
Prepare a frequency distribution table and extend it to a
cumulative frequency distribution and cumulative percentage
frequency distribution tables for the above data by using a
class interval of 5.
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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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