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Grade: 12th pass
        
all the values of a for which the quadratic expression ax^2 +(a-2)x -2 is negative for exactly two integral values f(x). lie in the interval -
 
5 months ago

Answers : (1)

Aditya Gupta
1716 Points
							
obviously a should be positive else it would be negative for infinite values of x.
now, ax^2 +(a-2)x -2= (x+1)(ax – 2)= a(x+1)(x – 2/a) 
by using wavy curve we can draw its sign scheme and note that it is negative in the interval (1, 2/a)
obviously 0 is an integer in this interval and indeed f(0)= – 2 is negative. since there must e exactly 2 such integers, the next integer is 1, so
2/a should be greater than 1.
but 2/a should be less than 2 else there would be 3 such integers.
solving this above 2 inequalities, we get
a lies in interval [1, 2).
kindly approve :)
5 months ago
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