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If both roots of ax^2+ax+1 = 0 are less than 1, then find the Complete set value of “a”

If both roots of ax^2+ax+1 = 0 are less than 1, then find the Complete set value of “a”
 

Grade:11

1 Answers

Arun
25750 Points
4 years ago
Dear student
 
it can be written as x^2 + x + 1/a = 0
 
hence for both roots less than 1
 
-B/2A = 0 and f(1) > 0
 
-1/2 =0 and 2+ 1/a > 0
 
(a-4)/a >=0 and (2a + 1)/a > 0
 
a belongs to ( – infinity , 0) U (4 , infinity)  and a belongs to ( -infinity, -1/2) U (0, infinity)
 
Now intersection
 
hence a belongs to ( – infinity , -1/2) U (4 , infinity)

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